Results 221 to 230 of about 7,694 (263)
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Balancing the Generalized Eigenvalue Problem
SIAM Journal on Scientific and Statistical Computing, 1981An 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, 1976The 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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On the generalized eigenvalue problem
Proceedings of 1994 American Control Conference - ACC '94, 2005In 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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Generalized eigenvalue problem for interval matrices
Archiv der Mathematik, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Singh, Sarishti, Panda, Geetanjali
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Inexact Inverse Iteration for Generalized Eigenvalue Problems
BIT Numerical Mathematics, 2000To 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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An Algorithm for Generalized Matrix Eigenvalue Problems
SIAM Journal on Numerical Analysis, 1973A 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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A non-self -adjoint general matrix eigenvalue problem
Journal of Computational Physics, 1987The eigenvalue problem for the partial-wave Schrödinger equation with central-symmetric and complex potential is subject to numerical study, in order to be used in nuclear physics (in the frame work of an optical model). The algorithms use an approximation which approximates the \(L^ 2(0,\infty)\) eigenvalue problem by an \(L^ 2(0,A)\) problem, with ...
Delic, G. +2 more
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Neurodynamic Approach for Generalized Eigenvalue Problems
2006 International Conference on Computational Intelligence and Security, 2006This paper presents a novel neurodynamic approach for solving generalized eigenvalue problems. A series of neurodynamic systems are proposed for finding all eigenvectors to a given pair (A, B) of matrices. Dynamical analysis shows that each system is globally convergent to an exact eigenvector of the pair (A, B) and hence all the eigenvectors can be ...
Quanju Zhang, Fuye Feng, Fuxian Liu
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Generalized eigenvalue problem for non-compact generators
Reports on Mathematical Physics, 1973Abstract An expansion in generalized eigenvectors of non-compact generators, based on the asymptotic behaviour of the corresponding one-parameter operator groups, is constructed. In particular, such expansion exists for the infinitesimal translations of the Poincare group.
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Generalized Eigenvalue Problems for Rectangular Matrices
IMA Journal of Applied Mathematics, 1977Jennings, L. S., Osborne, M. R.
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