In this paper we deal with generalized eigenvalue problem of matrix ?$A(z)$? with elements which are polynomials of ?$z$?. The well known iterative methodsof Muller, Newton and Laguerre for finding the zeros of function ?$f(z) = {\rm det} A(z)$? are analyzed. Decompositions of the matrix ?$A(z)$? and its derivatives are introduced in order to simplify the computations of the values of ?$f(z)$? and its first and second derivatives. Comparative analysis gives some indicators about the rate of convergence, computer time and accuracy of the computed eigenvalues for each of the method used. The analysed methods proved generally to be stable, economical and easily applicable. Fortran subroutines and an example of main calling programme are added for Muller's and Laguerre's method which proved tyo be more efficient than Newton's.

Rights

URN

URN:NBN:SI:DOC-7A7FMX8B

COBISSID

7534425

Added

04.07.2023

Metadata

Citation

APA:

Bohte, Zvonimir, Grad, Janez (1982). Algorithms for the solution of the generalized eigenvalue problem. Informatica (Ljubljana), volume 6, l, str. 43-54. URN:NBN:SI:DOC-7A7FMX8B from http://www.dlib.si

MLA:

Bohte, Zvonimir, Grad, Janez. "Algorithms for the solution of the generalized eigenvalue problem." Informatica (Ljubljana) volume 6. l (1982) str. 43-54.
<http://www.dlib.si/?URN=URN:NBN:SI:DOC-7A7FMX8B>

Informatica
1977-
(Assembly record)