Results 221 to 230 of about 7,955 (262)

Computation of Selected Eigenvalues of Generalized Eigenvalue Problems

Journal of Computational Physics, 1993
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Nayar, Narinder, Ortega, James M.
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On the generalized eigenvalue problem

Proceedings of 1994 American Control Conference - ACC '94, 2005
In this paper we extend the notion of a normal and symmetric matrix to a pair of real matrices. We show that the familiar properties of a symmetric matrix extend to the symmetric pair. The extension of the Courant-Fischer theorem for the characterization of the eigenvalues of the symmetric matrix is generalized.
R. Aripirala, V.L. Syrmos
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Parallel eigenvalue computation for banded generalized eigenvalue problems

Parallel Computing, 2019
Abstract We consider generalized eigenvalue problems A x = B x λ with a banded symmetric matrix A and a banded symmetric positive definite matrix B. To reduce the generalized eigenvalue problem to standard form C y = y λ the algorithm proposed by Crawford is applied preserving the banded structure in C.
Michael Rippl, Bruno Lang, Thomas Huckle
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Balancing the Generalized Eigenvalue Problem

SIAM Journal on Scientific and Statistical Computing, 1981
An algorithm is presented for balancing the A and B matrices prior to computing the eigensystem of the generalized eigenvalue problem $Ax = \lambda Bx$. The three-step algorithm is specifically designed to precede the $QZ$-type algorithms, but improved performance is expected from most eigensystem solvers.
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A Stable Generalized Eigenvalue Problem

SIAM Journal on Numerical Analysis, 1976
The eigenvalue problem $Ax = \lambda Bx$ is considered where A and B are real symmetric matrices. Perturbation bounds are obtained in case the expression $(x^ * Ax)^2 + (x^ * Bx)^2 $ is bounded away from zero. Numerical methods for the solution of the problem are discussed.
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A new algorithm for the generalized eigenvalue problem

1997 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2002
The problem of finding the generalized eigenvalues and eigenvectors of a pair of real symmetric matrices A and B, with B>0, can be viewed as a smooth optimization problem on a smooth manifold. We present a cost function approach to the generalized eigenvalue problem which is posed on the product of the n-sphere and Euclidian space R. The critical point
Knut Hüper, Uwe Helmke
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An Algorithm for Generalized Matrix Eigenvalue Problems

SIAM Journal on Numerical Analysis, 1973
A new method, called the $QZ$ algorithm, is presented for the solution of the matrix eigenvalue problem $Ax = \lambda Bx$ with general square matrices A and B. Particular attention is paid to the degeneracies which result when B is singular. No inversions of B or its submatrices are used.
Moler, C. B., Stewart, G. W.
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Removal of infinite eigenvalues in the generalized matrix eigenvalue problem

Journal of Computational Physics, 1989
The generalized matrix eigenvalue problem (1) \([A(p)-\lambda B(p)]x=0\) is considered, where A, B are complex \(n\times n\) matrices depending on a parameter p, and B is singular. Two main approaches to solve this problem are known. Firstly one considers the reciprocal problem \((B-\mu A)x=0\) and secondly an alternative method which consists in a ...
Goussis, Dimitrios A., Pearlstein, Arne J.   +1 more
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The C-RISE algorithm and the generalized eigenvalue problem

[Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing, 1991
An order-recursive iterative algorithm (named the C-RISE algorithm, since it combines the C-RITE and RISE algorithms) is presented for the generalized eigendecomposition of a Hermitian pencil. An important feature is the inherent computational parallelism of the resulting algorithm, pointing to the potential for VLSI implementation. The order-recursive
A. A. (Louis) Beex, D. Mitchell Wilkes, Monique P. Fargues   +2 more
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Inexact Inverse Iteration for Generalized Eigenvalue Problems

BIT Numerical Mathematics, 2000
To solve the generalized eigenvalue problem \(Ax=\lambda Bx\), one can use the inverse iteration method where in each iteration a linear system of equation \(Az_{k+1}=Bx_k\), has to be solved. In recent years, it has been proposed to solve that system by iterative schemes leading to an inexact inverse iteration method.
Golub, Gene H., Ye, Qiang
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