Showing papers on "Divide-and-conquer eigenvalue algorithm published in 1966"
67 citations
35 citations
TL;DR: In this paper, an easily computable formula is given for calculating the sensitivity of an eigenvalue to changes in the matrix, which depends only on the eigen value of interest, the matrix and the changes of the matrix.
Abstract: An easily computable formula is given for calculating the sensitivity of an eigenvalue to changes in the matrix. This formula depends only on the eigenvalue of interest, the matrix and the changes in the matrix.
20 citations
TL;DR: Several methods have been proposed to determine the proper elements (i.e. eigenvalues and eigenfunctions) of Sturm-Liouville equations as discussed by the authors, and most of them have been reviewed by Kopal [1], but we shall examine one of them, the so called Rayleigh-Ritz method, in order to explain the main defect they have in common and to judge their general efficiency.
Abstract: where the values of the constants A1 , A2 and B1, B2 are not simultaneously zero. Several methods have been proposed to determine the proper elements (i.e. eigenvalues and eigenfunctions) of Sturm-Liouville equations. Most of them have been reviewed by Kopal [1], but we shall examine one of them, the so called Rayleigh-Ritz method, in order to explain the main defect they have in common and to judge their general efficiency. This method was originally proposed by Ritz [2]. By transformations whose details will not be given here but which are described in many classical texts it leads to the solutions of equations of the form:
19 citations
TL;DR: Modification of Potter method of Gaussian elimination for solving eigenvalue problems of buckling and free vibrations of shells of revolution is described in this article for solving the problem of free vibrations.
Abstract: Modification of Potter method of Gaussian elimination for solving eigenvalue problems of buckling and free vibrations of shells of revolution
18 citations
4 citations
1 citations