ISSN:
0029-5981
Keywords:
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
This paper presents an alternative to the subspace iteration and Lanczos techniques, both of which are now used to solve partial eigenvalues and eigenvectors of large generalized linear first order symmetric matrix systems. It is based on non-linear optimization of a modified Rayleigh quotient. The elements of the eigenvector are the decision variables. Orthogonality constraints with respect to the two matrices are incorporated in the sequential unconstrained optimization scheme. By imposing normality with respect to one of the matrices, the Hessian matrix reduces to a much simpler form for which the Woodburry transformation may be used. This, in combination with the fact that the banded structure of the matrices is maintained, results in a number of operations of the same order as the two standard methods. Shifting is readily integrated. Numerical comparison with existing techniques demonstrate the practicality of this method.
Additional Material:
7 Tab.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/nme.1620290303
