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Solving Symmetric Eigenvalue Problems
"... this paper were produced by Bob Dixon and Stephanie Dobler of PSC's Education and Training Group ..."
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this paper were produced by Bob Dixon and Stephanie Dobler of PSC's Education and Training Group
Symmetric Eigenvalue Problems on Multicore Architectures
, 2009
"... Reduction to condensed forms for symmetric eigenvalue problems on multicore architectures ..."
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Reduction to condensed forms for symmetric eigenvalue problems on multicore architectures
Direct Solvers for Symmetric Eigenvalue Problems
 IN MODERN METHODS AND ALGORITHMS OF QUANTUM CHEMISTRY, J. GROTENDORST (EDITOR), PROCEEDINGS, NIC SERIES VOLUME
, 2000
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ThickRestart Lanczos Method for Symmetric Eigenvalue Problems
 SIAM J. MATRIX ANAL. APPL
, 1998
"... For real symmetric eigenvalue problems, there are a number of algorithms that are mathematically equivalent, for example, the Lanczos algorithm, the Arnoldi method and the unpreconditioned Davidson method. The Lanczos algorithm is often preferred because it uses significantly fewer arithmetic ope ..."
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Cited by 23 (3 self)
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For real symmetric eigenvalue problems, there are a number of algorithms that are mathematically equivalent, for example, the Lanczos algorithm, the Arnoldi method and the unpreconditioned Davidson method. The Lanczos algorithm is often preferred because it uses significantly fewer arithmetic
Preconditioning the Lanczos algorithm for sparse symmetric eigenvalue problems
 SIAM J. Sci. Comput
, 1993
"... Abstract. A method for computing a few eigenpairs of sparse symmetric matrices is presented and analyzed that combines the power of preconditioning techniques with the efficiency of the Lanczos algorithm. The method is related to Davidson’s method and its generalizations, but can be less expensive f ..."
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Cited by 31 (2 self)
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Abstract. A method for computing a few eigenpairs of sparse symmetric matrices is presented and analyzed that combines the power of preconditioning techniques with the efficiency of the Lanczos algorithm. The method is related to Davidson’s method and its generalizations, but can be less expensive
An Arnoldi Method for Nonlinear Symmetric Eigenvalue Problems
 Proceedings of the SIAM Conference on Applied Linear Algebra
, 2002
"... this paper we consider the nonlinear eigenvalue problem T (#)x = 0 (1) where T (#) is a family of symmetric matrices depending on a parameter J , and J R is an open interval which may be unbounded. As in the linear case T (#) = #I A a parameter # is called an eigenvalue of T () if prob ..."
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Cited by 12 (7 self)
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this paper we consider the nonlinear eigenvalue problem T (#)x = 0 (1) where T (#) is a family of symmetric matrices depending on a parameter J , and J R is an open interval which may be unbounded. As in the linear case T (#) = #I A a parameter # is called an eigenvalue
CONVERGENCE ANALYSIS OF GRADIENT ITERATIONS FOR THE SYMMETRIC EIGENVALUE PROBLEM
"... Abstract. Gradient iterations for the Rayleigh quotient are simple and robust solvers to determine a few of the smallest eigenvalues together with the associated eigenvectors of (generalized) matrix eigenvalue problems for symmetric matrices. Sharp convergence estimates for the Ritz values and Ritz ..."
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Abstract. Gradient iterations for the Rayleigh quotient are simple and robust solvers to determine a few of the smallest eigenvalues together with the associated eigenvectors of (generalized) matrix eigenvalue problems for symmetric matrices. Sharp convergence estimates for the Ritz values and Ritz
page An Arnoldi Method for Nonlinear Symmetric Eigenvalue Problems
"... In this paper we consider the nonlinear eigenvalue problem T (λ)x = 0 (1) where T (λ) ∈ R n×n is a family of symmetric matrices depending on a parameter λ ∈ J, and J ⊂ R is an open interval which may be unbounded. As in the linear ..."
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In this paper we consider the nonlinear eigenvalue problem T (λ)x = 0 (1) where T (λ) ∈ R n×n is a family of symmetric matrices depending on a parameter λ ∈ J, and J ⊂ R is an open interval which may be unbounded. As in the linear
AFully Parallel Algorithm for the Symmetric Eigenvalue Problem
"... In this paper we present a parallel algorithm for the symmetric algebraic eigenvalue problem. The algorithm is based upon a divide and conquer scheme suggested by Cuppen for computing the eigensystem of a symmetric tridiagonal matrix. We extend this idea to obtain a parallel algorithm that retains ..."
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Cited by 1 (0 self)
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In this paper we present a parallel algorithm for the symmetric algebraic eigenvalue problem. The algorithm is based upon a divide and conquer scheme suggested by Cuppen for computing the eigensystem of a symmetric tridiagonal matrix. We extend this idea to obtain a parallel algorithm
Results 1  10
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