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337,656
Progress in the numerical solution of the nonsymmetric eigenvalue problem
, 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 ..."
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Cited by 10 (1 self)
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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
, 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 multicore 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
"... Abstract. In the dense nonsymmetric eigenvalue problem, work has focused on the Hessenberg reduction and QR iteration, using efficient algorithms and fast, Level 3 BLAS. Comparatively, computation of eigenvectors 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 algorithms and fast, Level 3 BLAS. Comparatively, computation of eigenvectors performs poorly, limited to slow, Level 2 BLAS performance with little speedup
On restarting the Arnoldi method for large nonsymmetric eigenvalue problems
 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 ..."
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Cited by 49 (9 self)
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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
, 1993
"... This paper describes a parallel algorithm for computing the eigenvalues and eigenvectors of a nonsymmetric matrix. The algorithm is based on a divideandconquer procedure and uses an iterative refinement technique. ..."
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Cited by 14 (3 self)
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This paper describes a parallel algorithm for computing the eigenvalues and eigenvectors of a nonsymmetric matrix. The algorithm is based on a divideandconquer procedure and uses an iterative refinement technique.
Numerical solution of large nonsymmetric eigenvalue problems
 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 ..."
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Cited by 21 (0 self)
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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
A Parallel Algorithm For The Nonsymmetric Eigenvalue Problems
"... 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
, 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 ..."
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Cited by 85 (0 self)
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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
, 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 ..."
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Cited by 10 (0 self)
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. 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