Extrapolating the Arnoldi Algorithm To Improve Eigenvector Convergence

zbMath1499.65003arXiv2103.08635MaRDI QIDQ5035918

L. Ridgway Scott, Sara Pollock

Publication date: 22 February 2022

Full work available at URL: https://arxiv.org/abs/2103.08635

zbMATH Keywords

extrapolationArnoldi algorithmeigenvalue computation

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Extrapolation to the limit, deferred corrections (65B05)

Uses Software

• SLEPc
• SparseMatrix
• lobpcg.m

Cites Work

• Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices
• Numerics of Gram-Schmidt orthogonalization
• A simple extrapolation method for clustered eigenvalues
• Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method
• The university of Florida sparse matrix collection
• Numerical methods for large eigenvalue problems
• SLEPc
• On the Rates of Convergence of the Lanczos and the Block-Lanczos Methods
• Van der Waals Interactions Between Two Hydrogen Atoms: The Slater--Kirkwood Method Revisited
• Deflation Techniques for an Implicitly Restarted Arnoldi Iteration
• Modified Gram-Schmidt (MGS), Least Squares, and Backward Stability of MGS-GMRES

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