RESTARTING TECHNIQUES FOR THE LANCZOS ALGORITHM AND THEIR IMPLEMENTATION IN PARALLEL COMPUTING ENVIRONMENTS: ARCHITECTURAL INFLUENCES

DOI10.1080/10637199808947378zbMath1003.65034OpenAlexW2172524341WikidataQ126248888 ScholiaQ126248888MaRDI QIDQ3146523

Maurice Clint, J. S. Weston, Marek Szularz

Publication date: 12 September 2002

Published in: Parallel Algorithms and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10637199808947378

zbMATH Keywords

numerical exampleseigenvectorsparallel computingLanczos algorithmextreme eigenvaluesperformanceseigenpairsreorthogonalizationrestarting techniquesvery large, sparse, symmetric matrices

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Parallel numerical computation (65Y05) Complexity and performance of numerical algorithms (65Y20)

Uses Software

• eigs
• ARPACK
• BLZPACK

Cites Work

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• The Lanczos algorithm for the generalized symmetric eigenproblem on shared-memory architectures
• Computing eigenvalues of very large symmetric matrices. An implementation of a Lanczos algorithm with no reorthogonalization
• A class of Lanczos-like algorithms implemented on parallel computers
• Some Perspectives on the Eigenvalue Problem
• Implicit Application of Polynomial Filters in a k-Step Arnoldi Method
• Error Analysis of the Lanczos Algorithm for Tridiagonalizing a Symmetric Matrix
• The simultaneous computation of a few of the algebraically largest and smallest eigenvalues of a large, sparse, symmetric matrix
• A Shifted Block Lanczos Algorithm for Solving Sparse Symmetric Generalized Eigenproblems
• MONITORING THE CONVERGENCE OF THE LANCZOS ALGORITHM IN PARALLEL COMPUTING ENVIRONMENTS
• Practical use of the symmetric Lanczos process with re-orthogonalization
• Determination of the Extreme Values of the Spectrum of a Bounded Self-Adjoint Operator