Fernando's solution to Wilkinson's problem: An application of double factorization

DOI10.1016/S0024-3795(97)80053-5zbMath0886.65033MaRDI QIDQ1373322

Beresford N. Parlett, Inderjit S. Dhillon

Publication date: 13 April 1998

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

zbMATH Keywords

algorithmnumerical exampleseigenvalueseigenvectorsGaussian eliminationsymmetric tridiagonal matrixdouble factorization

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15)

Related Items (max. 100)

Estimation of singular values of very large matrices using random sampling ⋮ On computing the eigenvectors of a class of structured matrices ⋮ The Singular Value Decomposition: Anatomy of Optimizing an Algorithm for Extreme Scale ⋮ Twisted factorization of a banded matrix ⋮ On a special basis of approximate eigenvectors with local supports for an isolated narrow cluster of eigenvalues of a symmetric tridiagonal matrix ⋮ Computing eigenvectors of block tridiagonal matrices based on twisted block factorizations ⋮ Multiple representations to compute orthogonal eigenvectors of symmetric tridiagonal matrices ⋮ Eigenpairs of Wilkinson Matrices ⋮ Relatively robust representations of symmetric tridiagonals ⋮ An implementation of the dqds algorithm (positive case) ⋮ Computation of Gauss-type quadrature formulas ⋮ A note on generating finer‐grain parallelism in a representation tree ⋮ The Godunov-inverse iteration: A fast and accurate solution to the symmetric tridiagonal eigenvalue problem ⋮ Computations of eigenpair subsets with the MRRR algorithm ⋮ Current inverse iteration software can fail ⋮ For tridiagonals \(T\) replace \(T\) with \(LDL\) ⋮ The orthogonal Rayleigh quotient iteration (ORQI) method ⋮ An \({\mathcal O}(n^{2})\) algorithm for the bidiagonal SVD ⋮ Localization and Pseudospectra of Twisted Toeplitz Matrices with Applications to Ion Channels ⋮ A real triple dqds algorithm for the nonsymmetric tridiagonal eigenvalue problem

Uses Software

• LAPACK

Cites Work

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• Analysis of a parallel solution method for tridiagonal linear systems
• A new look at the Lanczos algorithm for solving symmetric systems of linear equations
• Invariant subspaces for tightly clustered eigenvalues of tridiagonals
• Implicite difference methods for initial-boundary value problems
• Efficient Algorithms for Computing the Condition Number of a Tridiagonal Matrix
• Improving the Accuracy of Inverse Iteration
• A Review on the Inverse of Symmetric Tridiagonal and Block Tridiagonal Matrices
• On Computing an Eigenvector of a Tridiagonal Matrix. Part I: Basic Results
• Reliable Computation of the Condition Number of a Tridiagonal Matrix in O(n) Time
• On Fourier-Toeplitz Methods for Separable Elliptic Problems
• Inequalities on the Elements of the Inverse of a Certain Tridiagonal Matrix
• Numerical Stability in Problems of Linear Algebra
• Bounds for Eigenvalues of Certain Tridiagonal Matrices
• The Calculation of the Eigenvectors of Codiagonal Matrices

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