Works (8)
Updated: February 26th, 2024 08:09
2023 journal article
KRYLOV-AWARE STOCHASTIC TRACE ESTIMATION
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 44(3), 1218–1244.
author keywords: spectral function; Hutchinson's method; quadratic trace estimation; low-rank approximation; block-Lanczos method; Krylov subspace method
TL;DR:
An algorithm for estimating the trace of a matrix function using implicit products with a symmetric matrix using a Krylov subspace method based on a combination of deflation and stochastic trace estimation is introduced.
(via Semantic Scholar)
open access via arxiv.org (repository)
Source: Web Of Science
Added: October 16, 2023
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: Web Of Science, ORCID, 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 journal article
RANDOMIZED ALGORITHMS FOR ROUNDING IN THE TENSOR-TRAIN FORMAT
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 45(1), A74–A95.
author keywords: high-dimensional problems; randomized algorithms; tensor decompositions; tensortrain format
TL;DR:
Several randomized algorithms are proposed that are generalizations of randomized low-rank matrix approximation algorithms and provide significant reduction in computation compared to deterministic TT-rounding algorithms for rounding a sum of TT-tensors.
(via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: August 28, 2023
2022 journal article
A BLOCK BIDIAGONALIZATION METHOD FOR FIXED-ACCURACY LOW-RANK MATRIX APPROXIMATION
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 43(2), 661–680.
author keywords: block Lanczos; randomized algorithm; low-rank matrix approximation; fixed-accuracy problem
Source: Web Of Science
Added: January 23, 2023
2021 journal article
A multilevel approach to stochastic trace estimation
LINEAR ALGEBRA AND ITS APPLICATIONS, 638, 125–149.
author keywords: Spectral function; Trace estimation; Chebyshev approximation; Hutchinson's trace estimator; Multilevel Monte Carlo
Source: Web Of Science
Added: May 2, 2022
2020 journal article
SHARP 2-NORM ERROR BOUNDS FOR LSQR AND THE CONJUGATE GRADIENT METHOD
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 41(3), 1183–1207.
author keywords: LSQR; least-squares problem; sparse matrix; Krylov subspace method; Golub-Kahan process; conjugate gradient method; stopping criteria; iterative method
TL;DR:
This work considers the iterative method LSQR for solving $\min_x |Ax-b|_2$ and finds that at every step it produces an iterate that minimizes the norm of the norm.
(via Semantic Scholar)
Source: Web Of Science
Added: October 26, 2020
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