Works (150)
Updated: December 20th, 2024 10:45
2024 journal article
SMALL SINGULAR VALUES CAN INCREASE IN LOWER PRECISION\ast
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 45(3), 1518–1540.
author keywords: singular values; eigenvalues; arithmetic precision; perturbation theory; real sym-
open access via arxiv.org (repository)
Sources: ORCID, Web Of Science, NC State University Libraries
Added: August 15, 2024
2023 journal article
MONTE CARLO METHODS FOR ESTIMATING THE DIAGONAL OF A REAL SYMMETRIC MATRIX
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 44(1), 240–269.
author keywords: concentration inequalities; Monte Carlo methods; relative error; Rademacher random vectors; Gaussian random vectors
Sources: ORCID, Web Of Science, NC State University Libraries
Added: March 10, 2023
2023 article
Precision-aware deterministic and probabilistic error bounds for floating point summation
Hallman, E., & Ipsen, I. C. F. (2023, August 30). NUMERISCHE MATHEMATIK, Vol. 8.
author keywords: 65G99; 60G42; 60G50
Sources: Web Of Science, NC State University Libraries
Added: September 18, 2023
2023 journal article
Precision-aware deterministic and probabilistic error bounds for floating point summation
NUMERISCHE MATHEMATIK, 155(1-2), 83–119.
TL;DR:
A systematic recurrence for a martingale on a computational tree leads to explicit and interpretable bounds with nonlinear terms controlled explicitly rather than by big-O terms, which yields new deterministic and probabilistic error bounds for three classes of mono-precision algorithms.
(via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: December 4, 2023
2023 article
Statistical properties of BayesCG under the Krylov prior
Reid, T. W., Ipsen, I. C. F., Cockayne, J., & Oates, C. J. (2023, October 12). NUMERISCHE MATHEMATIK, Vol. 10.
author keywords: 15 A10
TL;DR:
Numerical experiments confirm that, under low-rank approximate Krylov posteriors, BayesCG is only slightly optimistic and exhibits the characteristics of a calibrated solver, and is computationally competitive with CG.
(via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: November 6, 2023
2021 article
A projector-based approach to quantifying total and excess uncertainties for sketched linear regression
Chi, J. T., & Ipsen, I. C. F. (2021, August 11). INFORMATION AND INFERENCE-A JOURNAL OF THE IMA, Vol. 8.
author keywords: expectation; variance; bias; mean squared error; predictive risk
TL;DR:
A projector-based approach to sketched linear regression is presented that is exact and that requires minimal assumptions on the sketching matrix, and enables derivation of key quantities from classic linear regression that account for the combined model- and algorithm-induced uncertainties.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
16. Peace, Justice and Strong Institutions
(OpenAlex)
Sources: ORCID, Web Of Science, NC State University Libraries
Added: November 17, 2021
2021 journal article
Multiplicative perturbation bounds for multivariate multiple linear regression in Schatten p-norms
LINEAR ALGEBRA AND ITS APPLICATIONS, 624, 87–102.
author keywords: Projector Multiplicative perturbations; Moore Penrose inverse; Schatten p-norms; Multivariate multiple linear; regression
TL;DR:
This work extends recent MLR analyses to sketched MMLR in general Schatten $p-norms by interpreting the sketched problem as a multiplicative perturbation, and derives expressions for the exact and perturbed solutions in terms of projectors for easy geometric interpretation.
(via Semantic Scholar)
Sources: ORCID, Web Of Science, NC State University Libraries
Added: May 1, 2021
2021 journal article
Probabilistic Iterative Methods for Linear Systems
Journal of Machine Learning Research. http://jmlr.org/papers/v22/21-0031.html
Source: ORCID
Added: November 17, 2021
2021 journal article
SEAGLE: A Scalable Exact Algorithm for Large-Scale Set-Based Gene-Environment Interaction Tests in Biobank Data
FRONTIERS IN GENETICS, 12.
author keywords: gene-based GxE test for biobank data; GxE collapsing test for biobank data; GxE test for large-scale sequencing data; scalable GEI test; gene-environment variance component test; gene-environment kernel test; regional-based gene-environment test
TL;DR:
SEAGLE, a Scalable Exact AlGorithm for Large-scale set-based G×E tests, is presented to permit GxE VC tests for biobank-scale data to explore the interaction of gene and physical activity status on body mass index and demonstrates its utility by conducting genome-wide gene-basedG×E analysis on the Taiwan Biobank data.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
14. Life Below Water
(OpenAlex)
Sources: Web Of Science, NC State University Libraries
Added: November 29, 2021
2021 journal article
SEAGLE: A Scalable Exact Algorithm for Large-Scale Set-based GxE Tests in Biobank Data
UN Sustainable Development Goal Categories
14. Life Below Water
(OpenAlex)
Source: ORCID
Added: May 14, 2021
2020 journal article
Probabilistic Error Analysis for Inner Products
SIAM Journal on Matrix Analysis and Applications, 41(4), 1726–1741.
author keywords: roundoff errors; random variables; concentration bounds; martingale; Azuma's inequality
TL;DR:
Probabilistic perturbation bounds as well as probabilistic roundoff error bounds for the sequential accumulation of the inner product are derived, giving a quantitative confirmation of Wilkinson's intuition.
(via Semantic Scholar)
Source: ORCID
Added: November 18, 2020
2019 journal article
A Bayesian conjugate gradient method
Bayesian Anal., 14(3), 937–1012.
Source: ORCID
Added: January 17, 2020
2019 article
Editorial: special edition on probabilistic numerics
Girolami, M., Ipsen, I. C. F., Oates, C. J., Owen, A. B., & Sullivan, T. J. (2019, November). STATISTICS AND COMPUTING, Vol. 29, pp. 1181–1183.
Contributors: M. Girolami *, I. Ipsen n, C. Oates *, A. Owen * & T. Sullivan*
TL;DR:
This special edition of Statistics and Computing is dedicated to the emerging field of Probabilistic Numerics, at the interface of statistical inference and numerical analysis, and accompanies the workshop on probabilistic numerics held in London, 11–13 April 2018.
(via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries, ORCID
Added: November 18, 2019
2019 journal article
LOW-RANK MATRIX APPROXIMATIONS DO NOT NEED A SINGULAR VALUE GAP
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 40(1), 299–319.
Contributors: P. Drineas* & I. Ipsen n
author keywords: singular value decomposition; principal angles; additive perturbations; multiplicative perturbations
TL;DR:
It is shown that the low-rank approximation errors, in the two-norm, Frobenius norm and more generally, any Schatten p- norm, are insensitive to additive rank-preserving perturbations in the projector basis; and to matrix perturbation that are additive or change the number of columns.
(via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: April 9, 2019
2019 journal article
Probabilistic linear solvers: a unifying view
STATISTICS AND COMPUTING, 29(6), 1249–1263.
Contributors: S. Bartels *, J. Cockayne *, I. Ipsen n & P. Hennig *
author keywords: Probabilistic linear solvers; Projection methods; Iterative methods; Preconditioning
TL;DR:
In this work surprisingly general conditions for equivalence of these disparate methods are presented, and connections between Probabilistic linear solvers and projection methods for linear systems are described, providing a probabilistic interpretation of a far more general class of iterative methods.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(Web of Science)
Sources: Web Of Science, NC State University Libraries, ORCID
Added: November 18, 2019
2018 journal article
A PROBABILISTIC SUBSPACE BOUND WITH APPLICATION TO ACTIVE SUBSPACES
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 39(3), 1208–1220.
Contributors: J. Holodnak*, I. Ipsen n & R. Smith n
author keywords: positive semidefinite matrices; principal angles; eigenvalue decomposition; eigen-value gaps; matrix concentration inequality; intrinsic dimension; Monte Carlo sampling; active sub-spaces
TL;DR:
This work presents a bound on the number of samples so that with high probability the angle between the dominant subspaces of E and S is less than a user-specified tolerance, and suggests that Monte Carlo sampling can be efficient in the presence of many parameters, as long as the underlying function f is sufficiently smooth.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: January 7, 2019
2018 journal article
Eigenvector Continuation with Subspace Learning
Physical Review Letters, 121(3).
Contributors: D. Frame n, R. He n, n , D. Lee *, D. Lee n & E. Rrapaj *
TL;DR:
While an eigenvector resides in a linear space with enormous dimensions, the eigen vector trajectory generated by smooth changes of the Hamiltonian matrix is well approximated by a very low-dimensional manifold, it is proved using analytic function theory and proposed an algorithm to solve for the extremal eigenvectors.
(via Semantic Scholar)
Sources: Crossref, NC State University Libraries, ORCID
Added: July 20, 2019
2018 journal article
STRUCTURAL CONVERGENCE RESULTS FOR APPROXIMATION OF DOMINANT SUBSPACES FROM BLOCK KRYLOV SPACES
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 39(2), 567–586.
Contributors: P. Drineas *, I. Ipsen n, E. Kontopoulou * & M. Magdon-Ismail *
author keywords: singular value decomposition; least squares; principal angles; gap-amplifying polynomials; random matrices
TL;DR:
The results presented here form the structural foundation for the analysis of randomized Krylov space methods, a combination of traditional Lanczos convergence analysis with optimal approximations via least squares problems.
(via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2017 journal article
Randomized matrix-free trace and log-determinant estimators
NUMERISCHE MATHEMATIK, 137(2), 353–395.
Contributors: A. Saibaba n , A. Alexanderian n & I. Ipsen n
TL;DR:
Random algorithms for estimating the trace and determinant of Hermitian positive semi-definite matrices and the error due to randomization are presented, for starting guesses whose elements are Gaussian or Rademacher random variables.
(via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries, ORCID
Added: August 6, 2018
2016 journal article
RandNLA, Pythons, and the CUR for your data problems: Reporting from G2S3 in Delphi
SIAM News, 49(1), 7–8.
Source: NC State University Libraries
Added: July 28, 2019
2015 journal article
CONDITIONING OF LEVERAGE SCORES AND COMPUTATION BY QR DECOMPOSITION
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 36(3), 1143–1163.
Contributors: J. Holodnak n, I. Ipsen n & T. Wentworth*
author keywords: principal angles; stable rank; condition number; row-scaling; componentwise perturbations
TL;DR:
The leverage scores of a full-column rank matrix A are the squared row norms of any orthonormal basis for range(A) and it is shown that corresponding leverage Scores of two matrices A and A + \Delta A are close in the relative sense, if they have large magnitude and if all principal angles between the column spaces of A & A are small.
(via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2015 journal article
RANDOMIZED APPROXIMATION OF THE GRAM MATRIX: EXACT COMPUTATION AND PROBABILISTIC BOUNDS
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 36(1), 110–137.
Contributors: J. Holodnak n & I. Ipsen n
author keywords: leverage scores; singular value decomposition; stable rank; coherence; matrix concentration inequalities; unbiased estimator
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2014 journal article
Preface
Linear Algebra and Its Applications, 464, 1–2.
Source: ORCID
Added: August 29, 2019
2014 journal article
THE EFFECT OF COHERENCE ON SAMPLING FROM MATRICES WITH ORTHONORMAL COLUMNS, AND PRECONDITIONED LEAST SQUARES PROBLEMS
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 35(4), 1490–1520.
Contributors: I. Ipsen & T. Wentworth*
author keywords: condition number; singular values; leverage scores; sums of random matrices; majorization; preconditioning; QR factorization
TL;DR:
A bound on the condition number of the sampled matrices in terms of the coherence $\mu$ of $Q$ is derived, which implies a, not necessarily tight, lower bound of $\mathcal{O}(m\mu\ln{n})$ for the number of sampled rows.
(via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2012 journal article
TL;DR:
Group Decision-Making Models for Sequential Tasks considers the “two-alternative forced-choice test,” where one must choose between two hypotheses: slimy green or yucky yellow; intruder or no intruder; and so on.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
16. Peace, Justice and Strong Institutions
(OpenAlex)
Source: ORCID
Added: August 29, 2019
2011 journal article
COMPUTING CHARACTERISTIC POLYNOMIALS FROM EIGENVALUES
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 32(1), 90–114.
Contributors: R. Rehman & I. Ipsen
author keywords: elementary symmetric functions; perturbation bounds; roundoff error bounds; determinant
TL;DR:
The roundoff error bounds imply that the Summation Algorithm is forward stable, and the running error bounds can be used to estimate the accuracy of the computed coefficients “on the fly,” and they tend to be less pessimistic than the round off error bounds.
(via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2011 journal article
ERGODICITY COEFFICIENTS DEFINED BY VECTOR NORMS
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 32(1), 153–200.
Contributors: I. Ipsen & T. Selee
author keywords: singular values; eigenvalues; stochastic matrices; nonnegative matrices; inclusion regions; projections
TL;DR:
It is shown that ergodicity coefficients can determine inclusion regions for subdominant eigenvalues of complex matrices, and that the tightness of these regions depends on the departure of the matrix from normality.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
10. Reduced Inequalities
(OpenAlex)
11. Sustainable Cities and Communities
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2011 journal article
Source: ORCID
Added: August 29, 2019
2011 journal article
TL;DR:
The two papers in this issue are concerned with analysis of differential equations: the solution of partial differential equations that describe heat transfer, while the second one analyzes hybrid dynamical systems whose behavior alternates between continuous and discrete modes.
(via Semantic Scholar)
Source: ORCID
Added: August 29, 2019
2011 journal article
Expository Research Papers
SIAM Review, 53(4), 721–721.
Source: ORCID
Added: January 17, 2020
2011 journal article
Expository Research Papers
SIAM Review, 53(3), 503–503.
Source: ORCID
Added: January 17, 2020
2011 article
Expository research papers
SIAM Review, Vol. 53. http://www.scopus.com/inward/record.url?eid=2-s2.0-84856706336&partnerID=MN8TOARS
Source: ORCID
Added: January 17, 2020
2011 journal article
IMPORTANCE SAMPLING FOR A MONTE CARLO MATRIX MULTIPLICATION ALGORITHM, WITH APPLICATION TO INFORMATION RETRIEVAL
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 33(4), 1689–1706.
Contributors: S. Eriksson-Bique, M. Solbrig, M. Stefanelli, S. Warkentin, R. Abbey* & I. Ipsen
author keywords: randomized algorithm; expected value; variance; term-by-document matrix; query matching
TL;DR:
Numerical experiments with query matching in information retrieval applications illustrate that the optimized probabilities produce more accurate matchings than the uniform probabilities and that they can also be computed efficiently.
(via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2011 journal article
RANK-DEFICIENT NONLINEAR LEAST SQUARES PROBLEMS AND SUBSET SELECTION
SIAM JOURNAL ON NUMERICAL ANALYSIS, 49(3), 1244–1266.
Contributors: I. Ipsen *, C. Kelley* & S. Pope
author keywords: nonlinear least squares; Levenberg-Marquardt algorithm; subset selection; singular value decomposition
TL;DR:
The local convergence of the Levenberg-Marquardt method is examined for the solution of nonlinear least squares problems that are rank-deficient and have nonzero residual to show that replacing the Jacobian by a truncated singular value decomposition can be numerically unstable.
(via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2010 journal article
Source: ORCID
Added: August 29, 2019
2010 journal article
Source: ORCID
Added: August 29, 2019
2010 journal article
UN Sustainable Development Goal Categories
7. Affordable and Clean Energy
(OpenAlex)
Source: ORCID
Added: August 29, 2019
2010 journal article
Expository Research Papers
SIAM Review, 52(1), 55–55.
Source: ORCID
Added: January 17, 2020
2010 article
Expository research papers
SIAM Review, Vol. 52. http://www.scopus.com/inward/record.url?eid=2-s2.0-79952956707&partnerID=MN8TOARS
Source: ORCID
Added: January 17, 2020
2010 conference paper
Rank-deficient and ill-conditioned nonlinear least squares problems
Proceedings of the 2010 East Asian SIAM Conference. Presented at the East Asian Society of Industrial and Applied Mathematics Conference.
Event: East Asian Society of Industrial and Applied Mathematics Conference
Source: NC State University Libraries
Added: March 17, 2021
2010 chapter
The Eigenproblem and Invariant Subspaces: Perturbation Theory
In G.W. Stewart (pp. 71–93).
Sources: Crossref, NC State University Libraries
Added: July 20, 2019
2009 journal article
ORDINAL RANKING FOR GOOGLE'S PAGERANK
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 30(4), 1677–1696.
Contributors: R. Wills* & I. Ipsen
author keywords: ranking distance; power method; stochastic matrix; PageRank; Google matrix; ordinal rank; roundoff error
TL;DR:
This work presents computationally efficient criteria that can guarantee correct ordinal ranking of Google's PageRank scores when they are computed with the power method, and discusses the tightness of the ranking criteria, and illustrates their effectiveness for top k and bucket ranking.
(via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2009 journal article
Source: ORCID
Added: August 29, 2019
2009 journal article
UN Sustainable Development Goal Categories
4. Quality Education
(OpenAlex)
Source: ORCID
Added: August 29, 2019
2009 journal article
Problems and Techniques
SIAM Review, 51(4), 705–705.
Source: ORCID
Added: January 17, 2020
2009 article
Problems and Techniques
Ipsen, I. (2009, February 5). SIAM Review, Vol. 51, pp. 127–127.
Source: ORCID
Added: January 17, 2020
2009 article
Problems and techniques
SIAM Review, Vol. 51. http://www.scopus.com/inward/record.url?eid=2-s2.0-59749092679&partnerID=MN8TOARS
Source: ORCID
Added: January 17, 2020
2009 article
REFINED PERTURBATION BOUNDS FOR EIGENVALUES OF HERMITIAN AND NON-HERMITIAN MATRICES
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, Vol. 31, pp. 40–53.
Contributors: I. Ipsen * & B. Nadler
author keywords: eigenvalues; Hermitian matrix; eigenvalue gap; perturbation bounds; non-Hermitian perturbations; principal components; numerical continuation
TL;DR:
Eigenvalue bounds for perturbations of Hermitian matrices are presented and the change in eigenvalues are expressed in terms of a projection of the perturbation onto a particular eigenspace, rather than in terms.
(via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2009 article
SPECIAL ISSUE ON ACCURATE SOLUTION OF EIGENVALUE PROBLEMS
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, Vol. 31, pp. VII-VII.
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2009 journal article
Special issue on accurate solution of eigenvalue problems
SIAM Journal on Matrix Analysis and Applications, 31(1). http://www.scopus.com/inward/record.url?eid=2-s2.0-73649094469&partnerID=MN8TOARS
Contributors: I. Ipsen
Source: ORCID
Added: August 29, 2019
2008 journal article
PERTURBATION BOUNDS FOR DETERMINANTS AND CHARACTERISTIC POLYNOMIALS
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 30(2), 762–776.
Contributors: I. Ipsen & R. Rehman n
author keywords: elementary symmetric functions; singular values; eigenvalues; condition number determinant
TL;DR:
absolute perturbation bounds for the coefficients of the characteristic polynomial of a complex matrix are derived and it is suggested that coefficients of normal matrices are better conditioned with regard to absolute perturbations than those of general matrices.
(via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2008 journal article
Preface to the 14th ILAS Conference Proceedings Shanghai 2007
Linear Algebra and Its Applications, 430(5-6).
Contributors: * , J. Moro *, P. Šemrl*, J. Shao*, P. Wu * & R. Brualdi *
Source: ORCID
Added: August 29, 2019
2008 journal article
UN Sustainable Development Goal Categories
15. Life on Land
(OpenAlex)
Source: ORCID
Added: August 29, 2019
2008 article
Problems and Techniques
Ipsen, I. (2008, January). SIAM Review, Vol. 50, pp. 35–35.
TL;DR:
The two papers in this issue deal with differential equations, one with the numerical solution of partial differential equation solutions, and the other one with analytic solutions for ordinary differential equations.
(via Semantic Scholar)
Source: ORCID
Added: January 17, 2020
2008 journal article
Problems and Techniques
SIAM Review, 50(4), 721–721.
Contributors: I. Ipsen
Source: ORCID
Added: August 29, 2019
2008 journal article
Source: ORCID
Added: August 29, 2019
2008 article
Problems and techniques
SIAM Review, Vol. 50. http://www.scopus.com/inward/record.url?eid=2-s2.0-50949105062&partnerID=MN8TOARS
Source: ORCID
Added: January 17, 2020
2007 journal article
Condition estimates for pseudo-arclength continuation
SIAM JOURNAL ON NUMERICAL ANALYSIS, 45(1), 263–276.
author keywords: pseudo-arclength continuation; singularity; GMRES; singular vectors; eigenvalues; rank-one update; turning point; simple fold; fold point; limit point
TL;DR:
The condition number of the Jacobian is bound in pseudo-arclength continuation problems, and the effect of this condition number on the linear system solution in a Newton-GMRES solve is quantified.
(via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018
2007 magazine article
First SIAG linear algebra school slated for July 2008
Ipsen, I. C. F. (2007, November 3). SIAM News, 40(9).
Source: NC State University Libraries
Added: March 17, 2021
2007 journal article
Pagerank computation, with special attention to dangling nodes
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 29(4), 1281–1296.
Contributors: I. Ipsen & T. Selee*
author keywords: stochastic matrix; stationary distribution; lumping; rank-one matrix; power method; Jordan decomposition; similarity transformation; Google
TL;DR:
A Jordan decomposition of the Google matrix for the (theoretical) extreme case when all Web pages are dangling nodes, when it is required to distinguish among different classes of dangling nodes.
(via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2007 journal article
Source: ORCID
Added: August 29, 2019
2007 article
Problems and Techniques
Ipsen, I. (2007, January). SIAM Review, Vol. 49, pp. 209–209.
Source: ORCID
Added: January 17, 2020
2007 journal article
UN Sustainable Development Goal Categories
14. Life Below Water
(OpenAlex)
Source: ORCID
Added: August 29, 2019
2007 journal article
Problems and Techniques
SIAM Review, 49(1), 33–34.
Source: ORCID
Added: January 17, 2020
2007 article
Problems and techniques
SIAM Review, Vol. 49. http://www.scopus.com/inward/record.url?eid=2-s2.0-34249999151&partnerID=MN8TOARS
Source: ORCID
Added: January 17, 2020
2007 journal article
Problems and techniques: Introduction
SIAM Review, 49(4). http://www.scopus.com/inward/record.url?eid=2-s2.0-37249005235&partnerID=MN8TOARS
Source: ORCID
Added: August 29, 2019
2007 article
Problems and techniques: Introduction
SIAM Review, Vol. 49. http://www.scopus.com/inward/record.url?eid=2-s2.0-37249005235&partnerID=MN8TOARS
Source: ORCID
Added: January 17, 2020
2006 journal article
Communicating Applied Mathematics: Four Examples
SIAM Review, 48(2), 359–389.
author keywords: education; mathematical writing; presentations; audience; peer critique
TL;DR:
A water-supply problem considered by the optimization and hydrology communities for benchmarking purposes is introduced and a nonclassical shock wave previously unknown to exist in thin liquid films is discovered.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
4. Quality Education
(OpenAlex)
6. Clean Water and Sanitation
(Web of Science)
11. Sustainable Cities and Communities
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries, Crossref
Added: August 6, 2018
2006 journal article
Convergence analysis of a PageRank updating algorithm by Langville and Meyer
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 27(4), 952–967.
Contributors: I. Ipsen & S. Kirkland
author keywords: Google; PageRank; Markov chain; power method; stochastic complement; aggregation/disaggregation
TL;DR:
By exploiting the hyperlink structure of the web it can be shown that the asymptotic convergence rate of the SIAD method applied to the Google matrix can be made strictly faster than that of the power method.
(via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2006 journal article
Mathematical properties and analysis of Google’s PageRank
Boletin De La Sociedad Espanola De Matematica Aplicada, 34, 191–196.
Source: NC State University Libraries
Added: July 10, 2019
2006 magazine article
New ideas for SIAM conferences from Europe
Ipsen, I. C. F. (2006, December). SIAM News, 39(10), 5.
Source: NC State University Libraries
Added: March 17, 2021
2006 journal article
Source: ORCID
Added: August 29, 2019
2006 journal article
Source: ORCID
Added: August 29, 2019
2006 journal article
Problems and Techniques
SIAM Review, 48(4), 679–680.
Source: ORCID
Added: January 17, 2020
2006 journal article
Problems and Techniques
SIAM Review, 48(2), 305–305.
Source: ORCID
Added: January 17, 2020
2006 article
Problems and techniques
SIAM Review, Vol. 48, pp. 41–42. http://www.scopus.com/inward/record.url?eid=2-s2.0-33644586567&partnerID=MN8TOARS
Source: ORCID
Added: January 17, 2020
2006 journal article
Problems and techniques: Introduction
SIAM Review, 48(2), 485–486. http://www.scopus.com/inward/record.url?eid=2-s2.0-33744920863&partnerID=MN8TOARS
Contributors: I. Ipsen
Source: ORCID
Added: August 29, 2019
2006 article
Problems and techniques: Introduction
SIAM Review, Vol. 48, pp. 485–486. http://www.scopus.com/inward/record.url?eid=2-s2.0-33744920863&partnerID=MN8TOARS
Source: ORCID
Added: January 17, 2020
2006 article
Special issue on accurate solution of eigenvalue problems
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, Vol. 28, pp. IX-IX.
TL;DR:
The twelve papers in the current issue are concerned with a variety of aspects that arise in the computation of eigenvalues and invariant subspaces: perturbation bounds and sensitivity, accuracy and convergence behavior of algorithms, exploitation of structure in matrices, and particular engineering applications.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
13. Climate Action
(OpenAlex)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2006 journal article
Special issue on accurate solution of eigenvalue problems
SIAM Journal on Matrix Analysis and Applications, 28(4). http://www.scopus.com/inward/record.url?eid=2-s2.0-35348933724&partnerID=MN8TOARS
Contributors: I. Ipsen
Source: ORCID
Added: August 29, 2019
2005 journal article
How to get SIAM cooperation for your meeting
SIAM News, 38(2).
Source: NC State University Libraries
Added: July 10, 2019
2005 journal article
Source: ORCID
Added: August 29, 2019
2005 article
Problems and techniques
SIAM Review, Vol. 47. http://www.scopus.com/inward/record.url?eid=2-s2.0-28244444106&partnerID=MN8TOARS
Source: ORCID
Added: January 17, 2020
2005 magazine article
Why aren’t SIAM conferences cheaper?
Ipsen, I. C. F. (2005, January). SIAM News, 38(1), 1.
Source: NC State University Libraries
Added: March 17, 2021
2004 magazine article
Accurate eigenvalues for fast trains
Ipsen, I. C. F. (2004, November). SIAM News, 37(9), 1–2.
Source: NC State University Libraries
Added: March 17, 2021
2003 journal article
Zone determinant expansions for nuclear lattice simulations
PHYSICAL REVIEW C, 68(6).
Contributors: D. Lee* & I. Ipsen *
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2002 article
A note on unifying absolute and relative perturbation bounds
Ipsen, I. C. F. (2003, January 1). LINEAR ALGEBRA AND ITS APPLICATIONS, Vol. 358, pp. 239–253.
Contributors: I. Ipsen n
author keywords: invariant subspace; eigenvalue; absolute bound; relative bound; subspace angle; departure from normality
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2002 article
Inclusion regions for matrix eigenvalues
Beattie, C., & Ipsen, I. C. F. (2003, January 1). LINEAR ALGEBRA AND ITS APPLICATIONS, Vol. 358, pp. 281–291.
Contributors: C. Beattie * & I. Ipsen n
author keywords: eigenvalue bounds; singular values; inclusion regions
UN Sustainable Development Goal Categories
10. Reduced Inequalities
(OpenAlex)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2001 journal article
A note on preconditioning nonsymmetric matrices
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 23(3), 1050–1051.
Contributors: I. Ipsen
author keywords: preconditioner; minimal polynomial
TL;DR:
The preconditioners for indefinite matrices of KKT form in [M.
(via Semantic Scholar)
Sources: ORCID, NC State University Libraries, Web Of Science
Added: August 6, 2018
2001 journal article
SIAG/LA and ILAS mark twenty years of progress at joint applied linear algebra meeting
SIAM News, 34(1).
Source: NC State University Libraries
Added: July 10, 2019
2001 journal article
Stability Radius and Optimal Scaling of Discrete-Time Periodic Systems
IFAC Proceedings Volumes, 34(12), 179–182.
Sources: Crossref, NC State University Libraries, ORCID
Added: July 27, 2019
2000 report
A note on a certain class of preconditioners for symmetric indefinite linear systems
(Technical Report No. M&CT-TECH-00-005). Mathematics & Computing Technology, Phantom Works Division, The Boeing Company.
Source: NC State University Libraries
Added: March 24, 2021
2000 article
Absolute and relative perturbation bounds for invariant subspaces of matrices
Ipsen, I. C. F. (2000, April 15). LINEAR ALGEBRA AND ITS APPLICATIONS, Vol. 309, pp. 45–56.
author keywords: invariant subspace; absolute error; relative error; eigenvalue separation; angle between subspaces
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2000 journal article
An overview of relative sin Theta theorems for invariant subspaces of complex matrices
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 123(1-2), 131–153.
Contributors: I. Ipsen n
author keywords: invariant subspace; eigenspace; relative bound; eigenvalues; grading; scaling
Sources: Web Of Science, ORCID
Added: August 6, 2018
2000 journal article
author keywords: linear system; Krylov space methods; GMRES; MINRES; Vandermonde matrix; eigenvalues; departure from normality
TL;DR:
It is shown that the minimal residual norm is large as long as the Krylov basis is well-conditioned and the residual norm for scaled Jordan blocks is expressed in terms of eigenvalues and departure from normality.
(via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: August 6, 2018
1998 report
A different approach to bounding the minimal residual norm in Krylov methods
(Technical Report No. CRSC-TR98-19). Raleigh, NC: Center for Research in Scientific Computation, Department of Mathematics, North Carolina State University.
Source: NC State University Libraries
Added: March 24, 2021
1998 report
A note on the field of values of non-normal matrices
(Technical Report No. CRSC-TR98-26). Raleigh, NC: Center for Research in Scientific Computation, Department of Mathematics, North Carolina State University.
Source: NC State University Libraries
Added: March 24, 2021
1998 report
If a matrix has a single eigenvalue, how sensitive is this eigenvalue?
(Technical Report No. CRSC-TR98-8). Raleigh, NC: Center for Research in Scientific Computation, Department of Mathematics, North Carolina State University.
Source: NC State University Libraries
Added: March 24, 2021
1998 journal article
Relative perturbation results for eigenvalues and eigenvectors of diagonalisable matrices
BIT, 38(3), 502–509.
Contributors: S. Eisenstat* & I. Ipsen n
author keywords: eigenvalue; eigenvector; condition number; relative error; diagonalisable matrix; angle between subspaces
Sources: Web Of Science, ORCID
Added: August 6, 2018
1998 journal article
Relative perturbation results for matrix eigenvalues and singular values
Acta Numerica, 7, 151–201.
Contributors: I. Ipsen n
Sources: Crossref, NC State University Libraries, ORCID
Added: July 20, 2019
1998 journal article
The idea behind Krylov methods
AMERICAN MATHEMATICAL MONTHLY, 105(10), 889–899.
Contributors: I. Ipsen n & C. Meyer n
Sources: Web Of Science, ORCID
Added: August 6, 2018
1998 journal article
The lack of influence of the right-hand side on the accuracy of linear system solution
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 20(1), 203–227.
author keywords: linear system; right-hand side; condition number; backward error; stopping criterion
TL;DR:
It is commonly believed that a fortunate right-hand side b can significantly reduce the sensitivity of a system of linear equations Ax=b, but this is not true when the system is solved with Gaussian elimination or the QR factorization: the error bounds essentially do not depend on b, and the error itself seems to depend only weakly on b.
(via Semantic Scholar)
Sources: NC State University Libraries, ORCID, Web Of Science
Added: August 6, 2018
1998 journal article
The lack of influence of the right-hand side on the accuracy of linear system solution
SIAM Journal on Scientific Computing, 20(1), 203–227. http://www.scopus.com/inward/record.url?eid=2-s2.0-0032131636&partnerID=MN8TOARS
Contributors: J. Banoczi, N. Chiu, G. Cho & I. Ipsen
Source: ORCID
Added: August 29, 2019
1998 journal article
Three absolute perturbation bounds for matrix eigenvalues imply relative bounds
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 20(1), 149–158.
Contributors: S. Eisenstat* & I. Ipsen n
author keywords: eigenvalues; relative perturbation bounds; conditioning
TL;DR:
It is shown that eigenvalues of normal matrices are no more sensitive to perturbations than eigen values of Hermitian positive-definite matrices, and the relative error bounds are invariant under congruence transformations, such as grading and scaling.
(via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
1997 journal article
Computing an eigenvector with inverse iteration
SIAM REVIEW, 39(2), 254–291.
author keywords: eigenvector; invariant subspace; inverse iteration; departure from normality; ill-conditioned linear system
TL;DR:
It is concluded that the behavior of the residuals in inverse iteration is governed by the departure of the matrix from normality rather than by the conditioning of a Jordan basis or the defectiveness of eigenvalues.
(via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
1997 report
If a matrix has a single eigenvalue, how sensitive is this eigenvalue?
(Technical Report No. CRSC-TR97-20). Raleigh, NC: Center for Research in Scientific Computation, Department of Mathematics, North Carolina State University.
Source: NC State University Libraries
Added: March 24, 2021
1996 chapter
A history of inverse iteration
In H. Wielandt, B. Huppert, & H. Schneider (Eds.), Mathematische Werke. Vol. 2, Linear algebra and analysis : Mathematical works (pp. 464–472). Berlin: Walter de Gruyter.
Ed(s): H. Wielandt, B. Huppert & H. Schneider
Source: NC State University Libraries
Added: April 8, 2021
1996 journal article
Convergence Estimates for Solution of Integral Equations with GMRES
Journal of Integral Equations and Applications, 8(1), 19–34.
Contributors: S. Campbell* , I. Ipsen, C. Kelley* , C. Meyer & Z. Xue
Sources: Crossref, ORCID, NC State University Libraries
Added: July 20, 2019
1996 journal article
GMRES and the minimal polynomial
BIT Numerical Mathematics, 36(4), 664–675.
Contributors: S. Campbell n , I. Ipsen n, C. Kelley n & C. Meyer n
author keywords: GMRES; superlinear convergence; minimal polynomial; eigenvalue index
TL;DR:
A qualitative model for the convergence behaviour of the Generalised Minimal Residual (GMRES) method for solving nonsingular systems of linear equationsAx =b in finite and infinite dimensional spaces and bounds are provided that explain the convergence of GMRES.
(via Semantic Scholar)
Sources: Crossref, Web Of Science, NC State University Libraries, ORCID
Added: July 20, 2019
1996 chapter
Helmut Wielandt’s contributions to the numerical solution of complex eigenvalue problems
In B. Huppert & H. Schneider (Eds.), Helmut Wielandt, Mathematische Werke, Mathematical Works, volume 2: Linear Algebra and Analysis (pp. 453–463). Berlin: Walter de Gruyter.
Ed(s): B. Huppert & H. Schneider
Source: NC State University Libraries
Added: July 10, 2019
1995 journal article
Analysis of a QR Algorithm for Computing Singular Values
SIAM Journal on Matrix Analysis and Applications, 16(2), 520–535.
author keywords: SINGULAR VALUE DECOMPOSITION; EIGENVALUE DECOMPOSITION; QR DECOMPOSITION; RANK REVEALING QR DECOMPOSITION; URV DECOMPOSITION; DEFLATION
TL;DR:
The perturbation result for the smallest singular values of a triangular matrix is stronger than the traditional results because it guarantees high relative accuracy in the smallest plural values after an off-diagonal block of the matrix has been set to zero.
(via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 20, 2019
1995 journal article
On the Sensitivity of Solution Components in Linear Systems of Equations
SIAM Journal on Matrix Analysis and Applications, 16(1), 93–112.
author keywords: CONDITION NUMBER; DIAGONAL SCALING; FORWARD ERROR; LINEAR SYSTEM; LEAST SQUARES; PERTURBATION THEORY
TL;DR:
It is shown that for many classes of matrices the ill conditioning of the matrix is due to a few rows of the inverse only, which means that many of the solution components are computed more accurately than current analyses predict.
(via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 20, 2019
1995 journal article
Relative Perturbation Techniques for Singular Value Problems
SIAM Journal on Numerical Analysis, 32(6), 1972–1988.
Contributors: S. Eisenstat & I. Ipsen
author keywords: SINGULAR VALUE DECOMPOSITION; COMPONENTWISE RELATIVE PERTURBATIONS; DEFLATION CRITERIA; BIDIAGONAL MATRICES; BIACYCLIC MATRICES
Sources: Crossref, ORCID, NC State University Libraries
Added: July 20, 2019
1995 journal article
The Angle Between Complementary Subspaces
The American Mathematical Monthly, 102(10), 904–911.
Sources: Crossref, NC State University Libraries
Added: July 20, 2019
1994 journal article
A divide and conquer algorithm for computing singular values
Zeitschrift Für Angewandte Mathematik Und Mechanik, 74(6), 532–534.
Source: NC State University Libraries
Added: April 8, 2021
1994 journal article
Backward errors for eigenvalue and singular value decompositions
Numerische Mathematik, 68(2), 215–223.
Contributors: S. Chandrasekaran* & I. Ipsen *
Sources: Crossref, ORCID, NC State University Libraries
Added: July 27, 2019
1994 journal article
On Rank-Revealing Factorisations
SIAM Journal on Matrix Analysis and Applications, 15(2), 592–622.
author keywords: CONDITION ESTIMATION; PIVOTING; ORTHOGONAL FACTORIZATION; NUMERICAL RANK; SINGULAR VALUES
TL;DR:
A systematic treatment of algorithms for determining RRQR factorisations and presents "hybrid" algorithms that solve the optimisation problems almost exactly (up to a factor proportional to the size of the matrix).
(via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 27, 2019
1994 chapter
On the singular value decomposition of triangular matrices
In J. Er-xiong (Ed.), Numerical algebra : proceedings of '92 Shanghai International Numerical Algebra and its Applications Conference (pp. 85–89). Shanghai: China Science and Technology Press.
Ed(s): J. Er-xiong
Event: Shanghai International Numerical Algebra and its Applications Conference at Shanghai
Source: NC State University Libraries
Added: April 8, 2021
1994 conference paper
Relative perturbation bounds for eigenspaces and singular vector subspaces
In J. G. Lewis (Ed.), Proceedings of the Fifth SIAM Conference on Applied Linear Algebra (pp. 62–65). Philadelphia: SIAM.
Ed(s): J. Lewis
Event: Fifth SIAM Conference on Applied Linear Algebra at Snowbird, Utah on June 15-18, 1994
Source: NC State University Libraries
Added: April 8, 2021
1994 journal article
Uniform Stability of Markov Chains
SIAM Journal on Matrix Analysis and Applications, 15(4), 1061–1074.
author keywords: MARKOV CHAINS; STATIONARY DISTRIBUTION; STOCHASTIC MATRIX; SENSITIVITY ANALYSIS; PERTURBATION THEORY; STABILITY OF A MARKOV CHAIN; CONDITION NUMBERS
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(Web of Science)
Sources: Crossref, NC State University Libraries
Added: July 27, 2019
1992 journal article
Improving the Accuracy of Inverse Iteration
SIAM Journal on Scientific and Statistical Computing, 13(2), 550–572.
author keywords: SYMMETRICAL TRIDIAGONAL EIGENVALUE PROBLEM; INVERSE ITERATION; EISPACK
TL;DR:
A statistical analysis and the results of numerical experiments are presented to show that the numerical accuracy of this new implementation of TINVIT is competitive with that of the implementations of the divide-and-conquer and QL methods.
(via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 27, 2019
1991 report
Perturbation Theory for the Solution of Systems of Linear Equations
Sources: Crossref, NC State University Libraries
Added: July 27, 2019
1991 chapter
Some Remarks on the Generalised Bareiss and Levinson Algorithms
In Numerical Linear Algebra, Digital Signal Processing and Parallel Algorithms (pp. 189–214).
TL;DR:
It is shown in this paper that the generalised Levinson algorithm is a direct consequence of the generalisation Bareiss algorithm, thereby considerably simplifying its presentation in comparison to previous work.
(via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 27, 2019
1990 chapter
From Bareiss' algorithm to the stable computation of partial correlations
In Advances in Parallel Computing (Vol. 1, pp. 53–91).
Contributors: J. Delosme & I. Ipsen
Source: ORCID
Added: January 17, 2020
1990 journal article
Solving the Symmetric Tridiagonal Eigenvalue Problem on the Hypercube
SIAM Journal on Scientific and Statistical Computing, 11(2), 203–229.
TL;DR:
This paper describes implementations of Cuppen's method, bisection, and multisection for the computation of all eigenvalues and eigenvectors of a real symmetric tridiagonal matrix on a distributed-memory hypercube multiprocessor.
(via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 27, 2019
1989 chapter
A Gray code scheme for local uniform mesh refinement on hypercubes
In Parallel Processing for Scientific Computing (pp. 202–206). Philadelphia: Society for Industrial and Applied Mathematics.
Source: NC State University Libraries
Added: July 10, 2019
1989 journal article
From Bareiss' algorithm to the stable computation of partial correlations
Journal of Computational and Applied Mathematics, 27(1-2), 53–91.
Contributors: J. Delosme * & I. Ipsen *
TL;DR:
A new algorithm is presented for the stable computation of sample partial correlation coefficients for symmetric positive-definite matrices B by generalizing Bareiss' algorithm for the solution of linear systems of equations with (non-symmetric) Toeplitz coefficient matrix to matrices that are not ToEplitz, and showing that it computes their LU and UL factorizations.
(via Semantic Scholar)
Sources: ORCID, Crossref, NC State University Libraries
Added: July 27, 2019
1989 conference paper
Parallel computation of algorithms with uniform dependences
In J. Dongarra, P. Messina, D. C. Sorensen, & R. G. Voigt (Eds.), Proceedings of the Fourth SIAM Conference on Parallel Processing for Scientific Computing (pp. 319–326). Philadelphia: Society for Industrial and Applied Mathematics.
Ed(s): J. Dongarra, P. Messina, D. Sorensen & R. Voigt
Event: Fourth SIAM Conference on Parallel Processing for Scientific Computing at Chicago, IL on December 11-13, 1989
Source: NC State University Libraries
Added: April 8, 2021
1989 journal article
TL;DR:
A new form of Gray-code is described which is called aninterleaved Gray- code that allows easy labeling of graph nodes when the maximal level of refinement is unknown, allows easy determination of nearby nodes in the graph, is completely deterministic, and often distributes the graph uniformly across a hypercube.
(via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 27, 2019
1988 conference paper
SAGA and CONDENSE: a two-phase approach for the implementation of recurrence equations on multiprocessor architectures
[1988] Proceedings of the Twenty-First Annual Hawaii International Conference on System Sciences. Volume I: Architecture Track, 126–130.
Contributors: J. Delosme * & *
Event: [1988] Proceedings of the Twenty-First Annual Hawaii International Conference on System Sciences. Volume I: Architecture Track
TL;DR:
The automation of parallel implementations of algorithms, specifically those arising in scientific and engineering applications, is investigated, and how these properties are utilized to generate efficient, and in certain cases optimal, schedules and processor assignments on particular multiprocessor configurations is investigated.
(via Semantic Scholar)
Sources: Crossref, ORCID
Added: July 28, 2019
1988 chapter
Systolic Algorithms for the Parallel Solution of Dense Symmetric Positive-Definite Toeplitz Systems
In The IMA Volumes in Mathematics and Its Applications (pp. 85–108).
TL;DR:
The most popular method for the solution of linear systems of equations with Toeplitz coefficient matrix on a single processor is Levinson’s algorithm, but it is not amenable to efficient parallel implementation, so use of the Schur algorithm makes it possible to perform the entire solution procedure on one processor array in time linear in the order of the matrix.
(via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 28, 2019
1988 report
The Cholesky factorization, Schur complements, correlation coefficients, angles between vectors, and the QR factorization
(Research Report No. 607). New Haven, Connecticut: Department of Computer Science, Yale University.
Source: NC State University Libraries
Added: October 24, 2021
1987 chapter
A comparison of Cuppen’s method and multisection for the solution of tridiagonal eigenvalue problems on the hypercube
In Advances in Computer Methods for Partial Differential Equations VI (pp. 425–430). The Institute for Mathematics and Computer Science.
Source: NC State University Libraries
Added: July 10, 2019
1987 report
Computing partial correlations from the data matrix
(Research Report No. 541). New Haven, Connecticut: Department of Computer Science, Yale University.
Source: NC State University Libraries
Added: October 24, 2021
1987 chapter
Efficient systolic arrays for the solution of Toeplitz systems: An illustration of a methodology for the construction of systolic architectures in VLSI
In Systolic Arrays (pp. 37–46). Adam Hilger.
Source: NC State University Libraries
Added: October 24, 2021
1987 report
ParLance: A para-functional programming environment for parallel and distributed computing
(Research Report No. 524). New Haven, Connecticut: Department of Computer Science, Yale University.
Source: NC State University Libraries
Added: October 24, 2021
1987 journal article
Scaled Givens Rotations for the Solution of Linear Least Squares Problems on Systolic Arrays
SIAM Journal on Scientific and Statistical Computing, 8(5), 716–733.
TL;DR:
A class of Scaled Givens rotations, to be applied to the solution of weighted multiple linear least squares problems on systolic arrays, is discussed, indicating slightly less accumulation of round off error than known sequential methods.
(via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 28, 2019
1987 chapter
Two methods for solving the symmetric tridiagonal eigenvalue problem on the hypercube
In Hypercube Multiprocessors (pp. 627–638). Society for Industrial and Applied Mathematics.
Source: NC State University Libraries
Added: October 24, 2021
1986 journal article
Complexity of dense-linear-system solution on a multiprocessor ring
Linear Algebra and Its Applications, 77(C), 205–239.
Contributors: I. Ipsen *, Y. Saad * & M. Schultz*
TL;DR:
The objective is to compare a variety of algorithms, which are fairly reasonable to program and to analyze, for the solution of a single problem on a certain class of parallel architectures, thereby leading to a more realistic approach to future algorithm development on multiprocessor machines.
(via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 28, 2019
1986 conference paper
Design Methodology For Systolic Arrays
In J. M. Speiser (Ed.), Advanced Algorithms and Architectures for Signal Processing I (Vol. 696, pp. 245–259).
Contributors: J. Delosme * & *
Ed(s): J. Speiser
Event: 30th Annual Technical Symposium
TL;DR:
The first elements of such a theory are presented in this paper, which aims to provide a general theory for more general coupled systems of affine recurrence equations.
(via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 28, 2019
1986 journal article
Parallel solution of symmetric positive definite systems with hyperbolic rotations
Linear Algebra and Its Applications, 77(C), 75–111.
Contributors: J. Delosme * & I. Ipsen *
TL;DR:
A systolic (VLSI) architecture implementing the resulting recurrence equations is more efficient than previously proposed pipelined Toeplitz system solvers and is amenable to implementation on a variety of parallel and vector machines.
(via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 28, 2019
1986 chapter
Systolic array synthesis: Computability and time cones
In Parallel Algorithms and Architectures (pp. 295–312). Amsterdam: North-Holland Publishing.
Source: NC State University Libraries
Added: October 28, 2021
1986 report
Systolic implementation of a Toeplitz system solver
(Research Report No. 8607). New Haven, Connecticut: Department of Electrical Engineering, Yale University.
Source: NC State University Libraries
Added: October 28, 2021
1986 chapter
The Impact of Parallel Architectures on The Solution of Eigenvalue Problems
In Large Scale Eigenvalue Problems, Proceedings of the IBM Europe Institute Workshop on Large Scale Eigenvalue Problems (Vol. 127, pp. 37–49).
Contributors: I. Ipsen * & Y. Saad *
TL;DR:
This paper presents a short survey of recent work on parallel implementations of Numerical Linear Algebra algorithms with emphasis on those relating to the solution of the symmetric eigenvalue problem on loosely coupled multiprocessor architectures.
(via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 28, 2019
1985 conference paper
An illustration of a methodology for the construction of efficient systolic architectures in VLSI
Proceedings of the Second International Symposium on VLSI Technology, Systems and Applications, 268–273.
Event: Second International Symposium on VLSI Technology, Systems and Applications at Taipei, Taiwan
Source: NC State University Libraries
Added: October 28, 2021
1985 report
How to embed trees in hypercubes
(Research Report No. 443). New Haven, Connecticut: Department of Computer Science, Yale University.
Source: NC State University Libraries
Added: July 10, 2019
1984 report
A parallel QR method using fast Givens’ rotations
(Research Report No. 299). New Haven, Connecticut: Department of Computer Science, Yale University.
Source: NC State University Libraries
Added: October 28, 2021
1984 conference paper
Singular Value Decomposition With Systolic Arrays
In K. Bromley (Ed.), Real-Time Signal Processing VII.
Ed(s): K. Bromley
Event: 28th Annual Technical Symposium
TL;DR:
Systolic arrays for determining the Singular Value Decomposition of a mxn, m > n, matrix A of bandwidth w are presented and the singular values of B are computed by the Golub-Reinsch iteration.
(via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 28, 2019
1983 journal article
Systolic Networks for Orthogonal Decompositions
SIAM Journal on Scientific and Statistical Computing, 4(2), 261–269.
TL;DR:
An orthogonally connected systolic array, consisting of a few types of simple processors, is constructed to perform the QR decomposition of a matrix and application is made to solution of linear systems and linear least squares problems as well asQL and LQ factorizations.
(via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 28, 2019
1982 conference paper
Systolic networks for orthogonal equivalence transformations and their applications
In P. Penfield (Ed.), Proceedings of the Conference on Advanced Research in VLSI (pp. 113–122). Norwood, MA: Artech House, Inc.
Ed(s): P. Penfield
Event: Conference on Advanced Research in VLSI
Source: NC State University Libraries
Added: October 28, 2021
Employment
Updated: December 11th, 2016 12:27
1993 - present
North Carolina State University Raleigh, NC, US
Professor
Mathematics
Education
Updated: December 11th, 2016 12:25
1978 - 1983
Pennsylvania State University University Park, PA, US
Ph.D.
Computer Science
Funding History
Funding history based on the linked ORCID record. Updated: October 15th, 2019 14:35
grant
August 15, 2018 - July 31, 2023
RTG: Randomized Numerical Analysis
Directorate for Mathematical & Physical Sciences
grant
August 1, 2018 - July 31, 2021
FRG: Collaborative Research: Randomization as a Resource for Rapid Prototyping
Directorate for Mathematical & Physical Sciences
grant
September 1, 2017 - August 31, 2020
Statistical and Applied Mathematical Sciences Institute
Directorate for Mathematical & Physical Sciences
grant
June 15, 2015 - May 31, 2016
2015 Gene Golub SIAM Summer School (G2S3): Randomization in Numerical Linear Algebra (RandNLA)
National Science Foundation - Directorate for Mathematical & Physical Sciences
grant
June 1, 2014 - May 31, 2016
Early-Career and Student Support for the XIX Householder Symposium, June 8-13, 2014
National Science Foundation - Directorate for Mathematical & Physical Sciences
grant
September 1, 2012 - August 31, 2018
Statistical and Applied Mathematical Sciences Institute
National Science Foundation - Directorate for Mathematical & Physical Sciences
grant
September 1, 2011 - November 30, 2014
EAGER: Numerical Accuracy of Randomized Algorithms for Matrix Multiplication and Least Squares
National Science Foundation - Directorate for Computer & Information Science & Engineering
grant
February 15, 2011 - January 31, 2012
Early Career and Student Support for the XVIII Householder Symposium
National Science Foundation - Directorate for Mathematical & Physical Sciences
grant
March 1, 2010 - February 28, 2011
Graduate Student Support for the 2010 Gene Golub Summer School in Italy
National Science Foundation - Directorate for Mathematical & Physical Sciences
grant
July 1, 2008 - June 30, 2009
Student and early career support for ISSNLA, July 20-25, 2008, Castro Urdiales, Spain
National Science Foundation - Directorate for Mathematical & Physical Sciences
grant
June 1, 2008 - May 31, 2009
Early Career Support for the Householder XVII Symposium
National Science Foundation - Directorate for Mathematical & Physical Sciences
grant
August 15, 2007 - July 31, 2016
Statistical and Applied Mathematical Sciences Institute
National Science Foundation - Directorate for Mathematical & Physical Sciences
grant
September 1, 2002 - August 31, 2004
Infinite-Dimensional Eigenvalue Problems
National Science Foundation - Directorate for Mathematical & Physical Sciences
grant
August 15, 2002 - July 31, 2005
Scientific Computing Research Environments for the Mathematical Sciences (SCREMS)
National Science Foundation - Directorate for Mathematical & Physical Sciences
grant
January 1, 2002 - December 31, 2007
Workup of the mathematical legacy of Helmut Wielandt
German Research Foundation
grant
June 1, 1998 - May 31, 2003
Joint NCSU-Boeing Academic-Industrial Research Project
National Science Foundation - Directorate for Mathematical & Physical Sciences
grant
September 15, 1994 - August 31, 1998
Relative Perturbation Techniques for Eigenvalue and Singular Value Decompositions
National Science Foundation - Directorate for Computer & Information Science & Engineering
grant
August 1, 1994 - July 31, 1995
Mathematical Sciences: Workshop on Krylov Subspace Methods and Applications
National Science Foundation - Directorate for Mathematical & Physical Sciences
grant
August 16, 1993 - July 31, 1995
Numerical Control Structures for the Computation of Large Eigenvalue and Singular Value Problems
National Science Foundation - Directorate for Computer & Information Science & Engineering
grant
August 15, 1991 - January 31, 1995
Numerical Control Structures for the Computation of Large Eigenvalue and Singular Value Problems
National Science Foundation - Directorate for Computer & Information Science & Engineering
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