Results 1 - 10 of 337,656

Progress in the numerical solution of the nonsymmetric eigenvalue problem

by Zhaojun Bai , 1993
"... With the growing demands from disciplinary and interdisciplinary fields of science and engineering for the numerical solution of the nonsymmetric eigenvalue problem, competitive new techniques have been developed for solving the problem. In this paper we examine the state of the art of the algorithm ..."
Abstract - Cited by 10 (1 self) - Add to MetaCart
With the growing demands from disciplinary and interdisciplinary fields of science and engineering for the numerical solution of the nonsymmetric eigenvalue problem, competitive new techniques have been developed for solving the problem. In this paper we examine the state of the art

Accelerating computation of eigenvectors in the nonsymmetric eigenvalue problem

by Mark Gates, Azzam Haidar, Jack Dongarra , 2014
"... In the nonsymmetric eigenvalue problem, work has focused on the Hessenberg reduction and QR iteration, using efficient algorithms and fast, Level 3 BLAS routines. Comparatively, computation of eigenvectors performs poorly, limited to slow, Level 2 BLAS performance with little speedup on multi-core s ..."
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In the nonsymmetric eigenvalue problem, work has focused on the Hessenberg reduction and QR iteration, using efficient algorithms and fast, Level 3 BLAS routines. Comparatively, computation of eigenvectors performs poorly, limited to slow, Level 2 BLAS performance with little speedup on multi

Accelerating computation of eigenvectors in the dense nonsymmetric eigenvalue problem

by Mark Gates, Azzam Haidar, Jack Dongarra
"... Abstract. In the dense nonsymmetric eigenvalue problem, work has focused on the Hessenberg reduction and QR iteration, using efficient al-gorithms and fast, Level 3 BLAS. Comparatively, computation of eigen-vectors performs poorly, limited to slow, Level 2 BLAS performance with little speedup on mul ..."
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Abstract. In the dense nonsymmetric eigenvalue problem, work has focused on the Hessenberg reduction and QR iteration, using efficient al-gorithms and fast, Level 3 BLAS. Comparatively, computation of eigen-vectors performs poorly, limited to slow, Level 2 BLAS performance with little speedup

On restarting the Arnoldi method for large nonsymmetric eigenvalue problems

by Ronald B. Morgan - Mathematics of Computation , 1996
"... Abstract. The Arnoldi method computes eigenvalues of large nonsymmetric matrices. Restarting is generally needed to reduce storage requirements and orthogonalization costs. However, restarting slows down the convergence and makes the choice of the new starting vector difficult if several eigenvalues ..."
Abstract - Cited by 49 (9 self) - Add to MetaCart
Abstract. The Arnoldi method computes eigenvalues of large nonsymmetric matrices. Restarting is generally needed to reduce storage requirements and orthogonalization costs. However, restarting slows down the convergence and makes the choice of the new starting vector difficult if several

A PARALLEL ALGORITHM FOR THE NONSYMMETRIC EIGENVALUE PROBLEM

by Jack J. Dongarra, Majed Sidani , 1993
"... This paper describes a parallel algorithm for computing the eigenvalues and eigenvectors of a nonsymmetric matrix. The algorithm is based on a divide-and-conquer procedure and uses an iterative refinement technique. ..."
Abstract - Cited by 14 (3 self) - Add to MetaCart
This paper describes a parallel algorithm for computing the eigenvalues and eigenvectors of a nonsymmetric matrix. The algorithm is based on a divide-and-conquer procedure and uses an iterative refinement technique.

Numerical solution of large nonsymmetric eigenvalue problems

by Youcef Saad - COMPUT. PHYS. COMM , 1989
"... We describe several methods on combinations of Krylov subspace techniques, deflation procedures and preconditionings, for computing a small number of eigenvalues and eigenvectors or Schur vectors of large sparse matrices. The most effective techniques for solving realistic problems from applications ..."
Abstract - Cited by 21 (0 self) - Add to MetaCart
We describe several methods on combinations of Krylov subspace techniques, deflation procedures and preconditionings, for computing a small number of eigenvalues and eigenvectors or Schur vectors of large sparse matrices. The most effective techniques for solving realistic problems from

Error analysis of the Lanczos algorithm for the nonsymmetric eigenvalue problem

by Zhaojun Bai , 1994
"... ..."
Abstract - Cited by 24 (3 self) - Add to MetaCart
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A Parallel Algorithm For The Nonsymmetric Eigenvalue Problems

by Richard Enbody, T. Y. Li, Xiaozhuo Yang
"... This paper presents a parallel algorithm to solve the eigenvalue problem for nonsymmetric matrices. The idea of homotopy is used to generate initial approximations, then the Aberth method and our modified Aberth method are used to find simultaneously all the eigenvalues. The advantage of this approa ..."
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This paper presents a parallel algorithm to solve the eigenvalue problem for nonsymmetric matrices. The idea of homotopy is used to generate initial approximations, then the Aberth method and our modified Aberth method are used to find simultaneously all the eigenvalues. The advantage

Rational Krylov algorithms for nonsymmetric Eigenvalue problems, II: Matrix pairs

by Axel Ruhe , 1992
"... A new algorithm for the computation of eigenvalues of a nonsymmetric matrix pencil is described. It is a generalization of the shifted and inverted Lanczos (or Arnoldi) algorithm, in which several shifts are used in one run. It computes an orthogonal basis and a small Hessenberg pencil. The eigensol ..."
Abstract - Cited by 85 (0 self) - Add to MetaCart
bifurcation problem arising from a hydrodynamical application are demonstrated. 1. INTRODUCTION We seek solutions to the generalized eigenvalue problem, (A \Gamma B)x = 0 ; (1) for large and sparse nonsymmetric matrices A and B. The matrices are too large to be treated by transformation methods

Homotopy Method For The Large Sparse Real Nonsymmetric Eigenvalue Problem

by S. H. Lui, H. B. Keller, T. W. C. Kwok , 1996
"... . A homotopy method to compute the eigenpairs, i.e., the eigenvectors and eigenvalues, of a given real matrix A1 is presented. From the eigenpairs of some real matrix A 0 , the eigenpairs of A(t) j (1 \Gamma t)A 0 + tA 1 are followed at successive "times" from t = 0 to t = 1 using contin ..."
Abstract - Cited by 10 (0 self) - Add to MetaCart
. A homotopy method to compute the eigenpairs, i.e., the eigenvectors and eigenvalues, of a given real matrix A1 is presented. From the eigenpairs of some real matrix A 0 , the eigenpairs of A(t) j (1 \Gamma t)A 0 + tA 1 are followed at successive "times" from t = 0 to t = 1 using
Results 1 - 10 of 337,656