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18,103
Dynamics of the symmetric eigenvalue problem with shift strategies
, 2011
"... A common algorithm for the computation of eigenvalues of real symmetric tridiagonal matrices is the iteration of certain special maps Fσ called shifted QR steps. Such maps preserve spectrum and a natural common domain is TΛ, the manifold of real symmetric tridiagonal matrices conjugate to the diagon ..."
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A common algorithm for the computation of eigenvalues of real symmetric tridiagonal matrices is the iteration of certain special maps Fσ called shifted QR steps. Such maps preserve spectrum and a natural common domain is TΛ, the manifold of real symmetric tridiagonal matrices conjugate
Discontinuous Plane Rotations and the Symmetric Eigenvalue Problem
, 2000
"... Elementary plane rotations are one of the building blocks of numerical linear algebra and are employed in reducing matrices to condensed form for eigenvalue computations and during the QR algorithm. Unfortunately, their implementation in standard packages such as EISPACK, the BLAS and LAPACK lack th ..."
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Elementary plane rotations are one of the building blocks of numerical linear algebra and are employed in reducing matrices to condensed form for eigenvalue computations and during the QR algorithm. Unfortunately, their implementation in standard packages such as EISPACK, the BLAS and LAPACK lack
NONLINEAR LOW RANK MODIFICATION OF A SYMMETRIC EIGENVALUE PROBLEM
"... Abstract. This paper studies existence and uniqueness results and interlacing properties of nonlinear modifications of small rank of symmetric eigenvalue problems. Approximation properties of the Rayleigh functional are used to design numerical methods the local convergence of which is quadratic or ..."
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Abstract. This paper studies existence and uniqueness results and interlacing properties of nonlinear modifications of small rank of symmetric eigenvalue problems. Approximation properties of the Rayleigh functional are used to design numerical methods the local convergence of which is quadratic
A JacobiDavidson Method for Solving ComplexSymmetric Eigenvalue Problems
 SIAM J. SCI. COMP
, 2002
"... We discuss variants of the JacobiDavidson method for solving the generalized complexsymmetric eigenvalue problem. The JacobiDavidson algorithm can be considered as an accelerated inexact Rayleigh quotient iteration. We show that it is appropriate to replace the Euclidean inner product x # y in ..."
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Cited by 9 (2 self)
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We discuss variants of the JacobiDavidson method for solving the generalized complexsymmetric eigenvalue problem. The JacobiDavidson algorithm can be considered as an accelerated inexact Rayleigh quotient iteration. We show that it is appropriate to replace the Euclidean inner product x # y
A comparison of the solution of the Symmetric Eigenvalue Problem with ScaLAPACK and Jacobi methods
"... In this paper we compare the performance obtained when solving the Symmetric Eigenvalue Problem with ScaLAPACK (routine pxsyevx) and with two blocked Jacobi methods on a Paragon. The conclusion is that when using a large number of processors a lower execution time is obtained with a Jacobi method th ..."
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Cited by 1 (1 self)
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In this paper we compare the performance obtained when solving the Symmetric Eigenvalue Problem with ScaLAPACK (routine pxsyevx) and with two blocked Jacobi methods on a Paragon. The conclusion is that when using a large number of processors a lower execution time is obtained with a Jacobi method
A Jacobi Method By Blocks To Solve The Symmetric Eigenvalue Problem
, 1997
"... In this paper, we demonstrate how considerable improvement in the performance of the Jacobi method for solving the symmetric eigenvalue problem can be obtained by reformulating the algorithm to be rich in matrixmatrix multiplication. To achieve this, we borrow techniques developed for parallel J ..."
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In this paper, we demonstrate how considerable improvement in the performance of the Jacobi method for solving the symmetric eigenvalue problem can be obtained by reformulating the algorithm to be rich in matrixmatrix multiplication. To achieve this, we borrow techniques developed for parallel
Complex WKB analysis of a PT symmetric eigenvalue problem
 J. Phys. A
"... The spectra of a particular class of PT symmetric eigenvalue problems has previously been studied, and found to have an extremely rich structure. In this paper we present an explanation for these spectral properties in terms of quantisation conditions obtained from the complex WKB method. In particu ..."
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Cited by 1 (0 self)
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The spectra of a particular class of PT symmetric eigenvalue problems has previously been studied, and found to have an extremely rich structure. In this paper we present an explanation for these spectral properties in terms of quantisation conditions obtained from the complex WKB method
A OneSided Jacobi Algorithm for the Symmetric Eigenvalue Problem
"... A method which uses onesided Jacobi to solve the symmetric eigenvalue problem in parallel is presented. We describe a parallel ring ordering for onesided Jacobi computation. One distinctive feature of this ordering is that it can sort column norms in each sweep, which is very important to achiev ..."
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Cited by 2 (1 self)
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A method which uses onesided Jacobi to solve the symmetric eigenvalue problem in parallel is presented. We describe a parallel ring ordering for onesided Jacobi computation. One distinctive feature of this ordering is that it can sort column norms in each sweep, which is very important
Condensed forms for the symmetric eigenvalue problem on multithreaded architectures
 Concurr. Comput. : Pract. Exper
, 2011
"... We investigate the performance of the routines in LAPACK and the Successive Band Reduction (SBR) toolbox for the reduction of a dense matrix to tridiagonal form, a crucial preprocessing stage in the solution of the symmetric eigenvalue problem, on generalpurpose multicore processors. In response to ..."
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Cited by 14 (3 self)
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We investigate the performance of the routines in LAPACK and the Successive Band Reduction (SBR) toolbox for the reduction of a dense matrix to tridiagonal form, a crucial preprocessing stage in the solution of the symmetric eigenvalue problem, on generalpurpose multicore processors. In response
LOWRANK TENSOR METHODS WITH SUBSPACE CORRECTION FOR SYMMETRIC EIGENVALUE PROBLEMS∗
"... Abstract. We consider the solution of largescale symmetric eigenvalue problems for which it is known that the eigenvectors admit a lowrank tensor approximation. Such problems arise, for example, from the discretization of highdimensional elliptic PDE eigenvalue problems or in strongly correlated ..."
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Cited by 9 (3 self)
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Abstract. We consider the solution of largescale symmetric eigenvalue problems for which it is known that the eigenvectors admit a lowrank tensor approximation. Such problems arise, for example, from the discretization of highdimensional elliptic PDE eigenvalue problems or in strongly correlated
Results 11  20
of
18,103