Updated: June 4th, 2023 05:00

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

Added: March 10, 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

Sources: ORCID, Web Of Science

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

Sources: ORCID, Web Of Science

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

Sources: Web Of Science, ORCID

Added: November 29, 2021

2021 journal article

SEAGLE: A Scalable Exact Algorithm for Large-Scale Set-based GxE Tests in Biobank Data

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

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.

Sources: Web Of Science, 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.

author keywords: singular value decomposition; principal angles; additive perturbations; multiplicative perturbations

Sources: Web Of Science, ORCID

Added: April 9, 2019

2019 journal article

Probabilistic linear solvers: a unifying view

*STATISTICS AND COMPUTING*, *29*(6), 1249–1263.

author keywords: Probabilistic linear solvers; Projection methods; Iterative methods; Preconditioning

Sources: Web Of Science, 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.

author keywords: positive semidefinite matrices; principal angles; eigenvalue decomposition; eigen-value gaps; matrix concentration inequality; intrinsic dimension; Monte Carlo sampling; active sub-spaces

Sources: Web Of Science, ORCID

Added: January 7, 2019

2018 journal article

Eigenvector Continuation with Subspace Learning

*Physical Review Letters*, *121*(3).

Sources: Crossref, 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.

author keywords: singular value decomposition; least squares; principal angles; gap-amplifying polynomials; random matrices

Sources: Web Of Science, ORCID

Added: August 6, 2018

2017 journal article

Randomized matrix-free trace and log-determinant estimators

*NUMERISCHE MATHEMATIK*, *137*(2), 353–395.

Sources: Web Of Science, 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.

author keywords: principal angles; stable rank; condition number; row-scaling; componentwise perturbations

Sources: Web Of Science, ORCID

Added: August 6, 2018

2015 journal article

Preface

*Linear Algebra and Its Applications*, *464*, 1–2.

Source: ORCID

Added: August 29, 2019

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.

author keywords: leverage scores; singular value decomposition; stable rank; coherence; matrix concentration inequalities; unbiased estimator

Sources: Web Of Science, ORCID

Added: August 6, 2018

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.

author keywords: condition number; singular values; leverage scores; sums of random matrices; majorization; preconditioning; QR factorization

Sources: Web Of Science, ORCID

Added: August 6, 2018

2012 journal article

Research spotlights

*SIAM Review*, *54*(1), 119–120.

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.

author keywords: elementary symmetric functions; perturbation bounds; roundoff error bounds; determinant

Sources: Web Of Science, ORCID

Added: August 6, 2018

2011 journal article

ERGODICITY COEFFICIENTS DEFINED BY VECTOR NORMS

*SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS*, *32*(1), 153–200.

author keywords: singular values; eigenvalues; stochastic matrices; nonnegative matrices; inclusion regions; projections

Sources: Web Of Science, ORCID

Added: August 6, 2018

2011 journal article

Expository Research Papers

*SIAM Review*, *53*(1), 69–69.

Source: ORCID

Added: August 29, 2019

2011 journal article

Expository Research Papers

*SIAM Review*, *53*(2), 289–289.

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.

author keywords: randomized algorithm; expected value; variance; term-by-document matrix; query matching

Sources: Web Of Science, ORCID

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.

author keywords: nonlinear least squares; Levenberg-Marquardt algorithm; subset selection; singular value decomposition

Sources: Web Of Science, ORCID

Added: August 6, 2018

2010 journal article

Expository Research Papers

*SIAM Review*, *52*(3), 453–453.

Source: ORCID

Added: August 29, 2019

2010 journal article

Expository Research Papers

*SIAM Review*, *52*(2), 267–267.

Source: ORCID

Added: August 29, 2019

2010 journal article

Expository Research Papers

*SIAM Review*, *52*(4), 675–675.

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, ORCID

Added: July 20, 2019

2009 journal article

Preface to the 14th ILAS Conference Proceedings Shanghai 2007

*Linear Algebra and Its Applications*, *430*(5-6).

Source: ORCID

Added: August 29, 2019

2009 journal article

Problems and Techniques

*SIAM Review*, *51*(2), 337–337.

Source: ORCID

Added: August 29, 2019

2009 journal article

Problems and Techniques

*SIAM Review*, *51*(3), 543–543.

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.

author keywords: eigenvalues; Hermitian matrix; eigenvalue gap; perturbation bounds; non-Hermitian perturbations; principal components; numerical continuation

Sources: Web Of Science, ORCID

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

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

Source: ORCID

Added: August 29, 2019

2008 journal article

ORDINAL RANKING FOR GOOGLE'S PAGERANK

*SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS*, *30*(4), 1677–1696.

author keywords: ranking distance; power method; stochastic matrix; PageRank; Google matrix; ordinal rank; roundoff error

Sources: Web Of Science, ORCID

Added: August 6, 2018

2008 journal article

PERTURBATION BOUNDS FOR DETERMINANTS AND CHARACTERISTIC POLYNOMIALS

*SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS*, *30*(2), 762–776.

author keywords: elementary symmetric functions; singular values; eigenvalues; condition number determinant

Sources: Web Of Science, ORCID

Added: August 6, 2018

2008 journal article

Problems and Techniques

*SIAM Review*, *50*(2), 273–273.

Source: ORCID

Added: August 29, 2019

2008 article

Problems and Techniques

Ipsen, I. (2008, January). *SIAM Review*, Vol. 50, pp. 35–35.

Source: ORCID

Added: January 17, 2020

2008 journal article

Problems and Techniques

*SIAM Review*, *50*(4), 721–721.

Source: ORCID

Added: August 29, 2019

2008 journal article

Problems and Techniques

*SIAM Review*, *50*(3), 483–483.

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

Sources: Web Of Science, ORCID

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.

author keywords: stochastic matrix; stationary distribution; lumping; rank-one matrix; power method; Jordan decomposition; similarity transformation; Google

Sources: Web Of Science, ORCID

Added: August 6, 2018

2007 journal article

Problems and Techniques

*SIAM Review*, *49*(4), 593–593.

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

Problems and Techniques

*SIAM Review*, *49*(3), 419–420.

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

Sources: Web Of Science, ORCID, 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.

author keywords: Google; PageRank; Markov chain; power method; stochastic complement; aggregation/disaggregation

Sources: Web Of Science, ORCID

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

Problems and Techniques

*SIAM Review*, *48*(1), 41–42.

Source: ORCID

Added: August 29, 2019

2006 journal article

Problems and Techniques

*SIAM Review*, *48*(3), 485–485.

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

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 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

Source: ORCID

Added: August 29, 2019

2006 article

Special issue on accurate solution of eigenvalue problems

*SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS*, Vol. 28, pp. IX-IX.

Sources: Web Of Science, ORCID

Added: August 6, 2018

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

Problems and Techniques

*SIAM Review*, *47*(4), 707–707.

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 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.

author keywords: invariant subspace; eigenvalue; absolute bound; relative bound; subspace angle; departure from normality

Sources: Web Of Science, ORCID

Added: August 6, 2018

2003 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.

author keywords: eigenvalue bounds; singular values; inclusion regions

Sources: Web Of Science, ORCID

Added: August 6, 2018

2003 journal article

Zone determinant expansions for nuclear lattice simulations

*PHYSICAL REVIEW C*, *68*(6).

Sources: Web Of Science, ORCID

Added: August 6, 2018

2001 journal article

A note on preconditioning nonsymmetric matrices

*SIAM JOURNAL ON SCIENTIFIC COMPUTING*, *23*(3), 1050–1051.

author keywords: preconditioner; minimal polynomial

Sources: ORCID, 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, 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

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.

author keywords: invariant subspace; eigenspace; relative bound; eigenvalues; grading; scaling

Sources: Web Of Science, ORCID

Added: August 6, 2018

2000 journal article

Expressions and bounds for the GMRES residual

*BIT*, *40*(3), 524–535.

author keywords: linear system; Krylov space methods; GMRES; MINRES; Vandermonde matrix; eigenvalues; departure from normality

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.

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.

Sources: Crossref, ORCID

Added: July 20, 2019

1998 journal article

The idea behind Krylov methods

*AMERICAN MATHEMATICAL MONTHLY*, *105*(10), 889–899.

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. http://www.scopus.com/inward/record.url?eid=2-s2.0-0032131636&partnerID=MN8TOARS

Source: ORCID

Added: August 29, 2019

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

Sources: ORCID, Web Of Science

Added: August 6, 2018

1998 journal article

Three absolute perturbation bounds for matrix eigenvalues imply relative bounds

*SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS*, *20*(1), 149–158.

author keywords: eigenvalues; relative perturbation bounds; conditioning

Sources: Web Of Science, ORCID

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

Sources: Web Of Science, ORCID

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.

Sources: Crossref, ORCID

Added: July 20, 2019

1996 journal article

GMRES and the minimal polynomial

*BIT Numerical Mathematics*, *36*(4), 664–675.

author keywords: GMRES; superlinear convergence; minimal polynomial; eigenvalue index

Sources: Crossref, Web Of Science, 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

Sources: Crossref, ORCID

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

Sources: Crossref, ORCID

Added: July 20, 2019

1995 journal article

Relative Perturbation Techniques for Singular Value Problems

*SIAM Journal on Numerical Analysis*, *32*(6), 1972–1988.

author keywords: SINGULAR VALUE DECOMPOSITION; COMPONENTWISE RELATIVE PERTURBATIONS; DEFLATION CRITERIA; BIDIAGONAL MATRICES; BIACYCLIC MATRICES

Sources: Crossref, ORCID

Added: July 20, 2019

1995 journal article

The Angle Between Complementary Subspaces

*The American Mathematical Monthly*, *102*(10), 904–911.

Sources: Crossref, ORCID

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.

Sources: Crossref, ORCID

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

Sources: Crossref, ORCID

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

Sources: Crossref, ORCID

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

Sources: Crossref, ORCID

Added: July 27, 2019

1991 report

Perturbation Theory for the Solution of Systems of Linear Equations

Sources: Crossref, ORCID

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).

Sources: Crossref, ORCID

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).

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.

Sources: Crossref, ORCID

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.

Sources: ORCID, Crossref

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

Recursive mesh refinement on hypercubes

*BIT*, *29*(2), 186–211.

Sources: Crossref, ORCID

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.

Event: [1988] Proceedings of the Twenty-First Annual Hawaii International Conference on System Sciences. Volume I: Architecture Track

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).

Sources: Crossref, ORCID

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.

Sources: Crossref, ORCID

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.

Sources: Crossref, ORCID

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).

Ed(s): J. Speiser

Event: 30th Annual Technical Symposium

Sources: Crossref, ORCID

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.

Sources: Crossref, ORCID

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).

Sources: Crossref, ORCID

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

Sources: Crossref, ORCID

Added: July 28, 2019

1983 journal article

Systolic Networks for Orthogonal Decompositions

*SIAM Journal on Scientific and Statistical Computing*, *4*(2), 261–269.

Sources: Crossref, ORCID

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

Updated: December 11th, 2016 12:27

1993 - present

Updated: December 11th, 2016 12:25

1978 - 1983

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