A backward stability analysis of diagonal pivoting methods for solving unsymmetric tridiagonal systems without interchanges

DOI10.1002/nla.674zbMath1249.65057OpenAlexW1996274087MaRDI QIDQ2889368

Roummel F. Marcia, Jennifer B. Erway

Publication date: 7 June 2012

Published in: Numerical Linear Algebra with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/nla.674

zbMATH Keywords

tridiagonal matrixnormwise backward stabilityunsymmetric indefinite factorization

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical computation of matrix norms, conditioning, scaling (65F35) Direct numerical methods for linear systems and matrix inversion (65F05)

Uses Software

• LAPACK
• mctoolbox

Cites Work

• Lanczos maximal algorithm for unsymmetric eigenvalue problems
• Stability of block LDL\(^T\) factorization of a symmetric tridiagonal matrix
• A composite step bi-conjugate gradient algorithm for nonsymmetric linear systems
• Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides
• On solving sparse symmetric linear systems whose definiteness is unknown
• Stability of the Diagonal Pivoting Method with Partial Pivoting
• Stable Factorizations of Symmetric Tridiagonal and Triadic Matrices
• A pivoting strategy for symmetric tridiagonal matrices
• A simplified pivoting strategy for symmetric tridiagonal matrices
• A Look-Ahead Lanczos Algorithm for Unsymmetric Matrices
• A Completed Theory of the Unsymmetric Lanczos Process and Related Algorithms, Part I
• Some Stable Methods for Calculating Inertia and Solving Symmetric Linear Systems
• Accurate Symmetric Indefinite Linear Equation Solvers
• Accuracy and Stability of Numerical Algorithms
• An Implementation of the Look-Ahead Lanczos Algorithm for Non-Hermitian Matrices
• Partial Pivoting Strategies for Symmetric Matrices