Stability of block \(LU\) factorization for block tridiagonal block \(H\)-matrices

DOI10.1016/j.cam.2012.01.003zbMath1237.65030OpenAlexW2085184732MaRDI QIDQ408202

Ting-Zhu Huang, Chi-Ye Wu

Publication date: 29 March 2012

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2012.01.003

zbMATH Keywords

stabilityperturbationrounding error analysisblock \(LU\) factorizationblock tridiagonal block \(H\)-matrices

Mathematics Subject Classification ID

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

Uses Software

• mctoolbox

Cites Work

• Perturbation bounds for the \(LDL^ H\) and LU decompositions
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• On the Perturbation of LU, Cholesky, and QR Factorizations
• Block Preconditioning for the Conjugate Gradient Method
• Average-Case Stability of Gaussian Elimination
• The stability of LU-decompositions of block tridiagonal matrices
• Growth in Gaussian Elimination
• Marching Algorithms for Elliptic Boundary Value Problems. I: The Constant Coefficient Case
• Iterative Solution Methods
• Exploiting fast matrix multiplication within the level 3 BLAS
• Stability of block algorithms with fast level-3 BLAS
• A Stable Method for the $LU$ Factorization of M-Matrices
• Stability of block LU factorization
• Stability of Symmetric Ill-Conditioned Systems Arising in Interior Methods for Constrained Optimization
• On Growth in Gaussian Elimination with Complete Pivoting
• Simultaneous backward stability of Gauss and Gauss–Jordan elimination
• Perturbation Theory for Factorizations of LU Type through Series Expansions
• On the Solution of Block-Tridiagonal Systems Arising from Certain Finite-Difference Equations
• Stability of a pivoting strategy for parallel Gaussian elimination
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