Updating the QR decomposition of block tridiagonal and block Hessenberg matrices

DOI10.1016/j.apnum.2007.04.010zbMath1143.65032OpenAlexW2079903960MaRDI QIDQ928841

Martin H. Gutknecht, Thomas Schmelzer

Publication date: 11 June 2008

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2007.04.010

zbMATH Keywords

eigenvalueseigenvectorsQR factorizationblock tridiagonal matrixblock Arnoldi processblock GMResblock Hessenberg matrixblock Krylov space methodblock Lanczos processblock MinResblock QMRblock SymmIQ

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical computation of eigenvalues and eigenvectors of matrices (65F15)

Related Items (7)

Optimal size of the block in block GMRES on GPUs: computational model and experiments ⋮ Inversion of Eddy-Current Signals Using a Level-Set Method and Block Krylov Solvers ⋮ Adaptively restarted block Krylov subspace methods with low-synchronization skeletons ⋮ Block tridiagonal reduction of perturbed normal and rank structured matrices ⋮ KSPHPDDM and PCHPDDM: extending PETSc with advanced Krylov methods and robust multilevel overlapping Schwarz preconditioners ⋮ Block Gram-Schmidt algorithms and their stability properties ⋮ A block MINRES algorithm based on the band Lanczos method

Uses Software

• CLARFG
• ABLE

Cites Work

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• A block QMR algorithm for non-Hermitian linear systems with multiple right-hand sides
• The block conjugate gradient algorithm and related methods
• The WY Representation for Products of Householder Matrices
• Block Reflectors: Theory and Computation
• Implementation Aspects of Band Lanczos Algorithms for Computation of Eigenvalues of Large Sparse Symmetric Matrices
• A Stabilized QMR Version of Block BiCG
• The computation of elementary unitary matrices
• A Lanczos-type method for multiple starting vectors
• ABLE: An Adaptive Block Lanczos Method for Non-Hermitian Eigenvalue Problems
• A Block QMR Method for Computing Multiple Simultaneous Solutions to Complex Symmetric Systems
• Analysis of Algorithms for Reflections in Bisectors

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