Parallel computation of the eigenvalues of symmetric Toeplitz matrices through iterative methods

DOI10.1016/j.jpdc.2008.03.003zbMath1243.65044OpenAlexW2002342892MaRDI QIDQ436859

Victor M. Garcia, Pedro Alonso, Miguel O. Bernabeu, Antonio M. Vidal

Publication date: 26 July 2012

Published in: Journal of Parallel and Distributed Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jpdc.2008.03.003

zbMATH Keywords

eigenvalue problemparallel computingToeplitz matricesShift-and-Invert Lanczos

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Iterative numerical methods for linear systems (65F10) Parallel numerical computation (65Y05) Toeplitz, Cauchy, and related matrices (15B05)

Related Items (2)

Strategies for spectrum slicing based on restarted Lanczos methods ⋮ An Inexact Shift-and-Invert Arnoldi Algorithm for Large Non-Hermitian Generalised Toeplitz Eigenproblems

Uses Software

• LAPACK
• Matlab
• ScaLAPACK
• JDQR
• JDQZ
• Sips

Cites Work

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• A high-performance, portable implementation of the MPI message passing interface standard
• The rational Krylov algorithm for nonlinear matrix eigenvalue problems
• Sine transform based preconditioners for symmetric Toeplitz systems
• Displacement ranks of a matrix
• SIPs
• Stability of Methods for Solving Toeplitz Systems of Equations
• Numerical Solution of the Eigenvalue Problem for Symmetric Rationally Generated Toeplitz matrices
• LAPACK Users' Guide
• PARALLEL ALGORITHMS TO COMPUTE THE EIGENVALUES AND EIGENVECTORS OFSYMMETRIC TOEPLITZ MATRICES∗
• A Shifted Block Lanczos Algorithm for Solving Sparse Symmetric Generalized Eigenproblems
• ScaLAPACK Users' Guide
• Templates for the Solution of Algebraic Eigenvalue Problems
• Fast Gaussian Elimination with Partial Pivoting for Matrices with Displacement Structure
• A symmetry exploiting Lanczos method for symmetric Toeplitz matrices

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