The use of a refined error bound when updating eigenvalues of tridiagonals

DOI10.1016/0024-3795(85)90213-7zbMath0629.65037OpenAlexW2008694421MaRDI QIDQ1094092

Beresford N. Parlett, Bahram Nour-Omid

Publication date: 1985

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(85)90213-7

zbMATH Keywords

convergenceeigenvaluesRitz valuesLanczos algorithmmisconvergencenested sequence of tridiagonal matrices

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Software, source code, etc. for problems pertaining to linear algebra (15-04)

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Cites Work

• A new look at the Lanczos algorithm for solving symmetric systems of linear equations
• A Divide and Conquer method for the symmetric tridiagonal eigenproblem
• Rank-one modification of the symmetric eigenproblem
• An invariant deflation for lower banded matrices
• The Lanczos Algorithm With Partial Reorthogonalization
• Lanczos versus subspace iteration for solution of eigenvalue problems
• The Spectral Transformation Lanczos Method for the Numerical Solution of Large Sparse Generalized Symmetric Eigenvalue Problems
• On Estimating the Largest Eigenvalue with the Lanczos Algorithm
• Error Analysis of the Lanczos Algorithm for Tridiagonalizing a Symmetric Matrix
• The Lanczos Algorithm with Selective Orthogonalization