Eric Hallman

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.

By: T. Chen * & E. Hallman n

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)
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.

By: E. Hallman n, I. Ipsen n  & A. Saibaba n 

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.

By: E. Hallman & I. Ipsen 

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.

By: E. Hallman n & I. Ipsen n 

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.

By: H. Al Daas *, G. Ballard *, P. Cazeaux *, E. Hallman n, A. Miedlar, M. Pasha *, T. Reid n, A. Saibaba n 

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.

By: E. Hallman*

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.

By: E. Hallman n & D. Troester n

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.

By: E. Hallman*

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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