Journal Article10.1007/BF01296239
Two-sided approximations in the LR-algorithm
TL;DR: An ALGOL program is derived for a modified LR-algorithm, permitting the determination of two-sided approximations to the eigenvalues of a tridiagonal symmetric matrix.
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Abstract: An ALGOL program is derived for a modified LR-algorithm, permitting the determination of two-sided approximations to the eigenvalues of a tridiagonal symmetric matrix. Test examples are considered.
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References
Householder's tridiagonalization of a symmetric matrix
TL;DR: In this article, an improved version of Householder's algorithm for tridiagonalization of a real symmetric matrix was discussed. But the most efficient form of the procedure depends on the method used to solve the eigenproblem of the derived tridiagon matrix.
112
Laguerre's Method Applied to the Matrix Eigenvalue Problem
TL;DR: In this paper, the authors present a new algorithm for the calculation of the eigenvalues of real square matrices of orders up to 100, which is directly applicable to complex matrices as well.
LR Algorithm with Laguerre Shift for Symmetric Tridiagonal Matrices
J. Grad,E. Zakrajšek +1 more
Abstract: This paper presents an algorithm for finding the eigenvalues of tridiagonal symmetric matrices. The method is in fact Laguerre's method modified in such a way that the explicit calculations of the coefficients of characteristic polynomial are avoided. Each eigenvalue is evaluated by the iterative process with cubic rate of convergence.
9
Tridiagonalization of a symetric band matrix
TL;DR: In this paper, Givens proposed the Jacobi rotation method to reduce a full symmetric matrix A = (a ik ) of order n by a sequence of appropriately chosen elementary orthogonal transformations (in the following called Jacobi rotations) to triput diagonal form.