Orthogonal similarity transformation of a symmetric matrix into a diagonal-plus-semiseparable one with free choice of the diagonal

DOI10.1007/s00211-005-0665-7zbMath1086.65040OpenAlexW2093019367MaRDI QIDQ818797

Raf Vandebril, Marc Van Barel, Ellen Van Camp, Nicola Mastronardi

Publication date: 21 March 2006

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-005-0665-7

zbMATH Keywords

computational complexityconvergencenumerical experimentsymmetric matrixreduction algorithmdiagonal-plus-semiseparable matrixorthogonal similarity transformation

Mathematics Subject Classification ID

Related Items (8)

Necessary and sufficient conditions for orthogonal similarity transformations to obtain the Arnoli(Lanczos)-Ritz values ⋮ A unification of unitary similarity transforms to compressed representations ⋮ Structured eigenvalue problems for rational Gauss quadrature ⋮ A Cholesky LR algorithm for the positive definite symmetric diagonal-plus-semiseparable eigenproblem ⋮ Eigen-solving via reduction to DPR1 matrices ⋮ Eigenvalue computation for unitary rank structured matrices ⋮ Linking the TPR1, DPR1 and arrow-head matrix structures ⋮ On the convergence properties of the orthogonal similarity transformations to tridiagonal and semiseparable (plus diagonal) form

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Inversion formulas and linear complexity algorithm for diagonal plus semiseparable matrices
• A Divide and Conquer method for the symmetric tridiagonal eigenproblem
• Direct and inverse eigenvalue problems for diagonal-plus-semiseparable matrices
• Two fast algorithms for solving diagonal-plus-semiseparable linear systems.
• Divide and conquer algorithms for computing the eigendecomposition of symmetric diagonal-plus-semiseparable matrices
• On the convergence properties of the orthogonal similarity transformations to tridiagonal and semiseparable (plus diagonal) form
• An implicit QR algorithm for symmetric semiseparable matrices
• Rational Krylov matrices and QR steps on Hermitian diagonal‐plus‐semiseparable matrices
• A note on the representation and definition of semiseparable matrices
• A Review on the Inverse of Symmetric Tridiagonal and Block Tridiagonal Matrices
• An Orthogonal Similarity Reduction of a Matrix into Semiseparable Form
• Fast and stable reduction of diagonal plus semi-separable matrices to tridiagonal and bidiagonal form

This page was built for publication: Orthogonal similarity transformation of a symmetric matrix into a diagonal-plus-semiseparable one with free choice of the diagonal