Sharper Probabilistic Backward Error Analysis for Basic Linear Algebra Kernels with Random Data

DOI10.1137/20M1314355zbMath1452.65090WikidataQ114615456 ScholiaQ114615456MaRDI QIDQ5132023

Nicholas J. Higham, Theo A. Mary

Publication date: 9 November 2020

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

zbMATH Keywords

floating-point arithmeticconcentration inequalitymatrix multiplicationrounding error analysisprobabilistic error boundsmean independence property

Mathematics Subject Classification ID

Roundoff error (65G50) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items

Matrix Multiplication in Multiword Arithmetic: Error Analysis and Application to GPU Tensor Cores, Mixed precision algorithms in numerical linear algebra, Floating-point arithmetic, Fast and accurate computation of the Euclidean norm of a vector, Precision-aware deterministic and probabilistic error bounds for floating point summation, Probabilistic Rounding Error Analysis of Householder QR Factorization, Five-Precision GMRES-Based Iterative Refinement, A Class of Fast and Accurate Summation Algorithms, Adaptive Precision Sparse Matrix–Vector Product and Its Application to Krylov Solvers, Numerical stability of algorithms at extreme scale and low precisions, Stochastic Rounding and Its Probabilistic Backward Error Analysis, Randomized Gram--Schmidt Process with Application to GMRES

Uses Software

• mctoolbox

Cites Work

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