ABSTRACT
The inverse power method evaluates the largest (in magnitude) eigenvalue of the inverse matrix, A-I. The general equation for the inverse power method is given by
A-I X = }'inversex (2.156)
This can be accomplished by evaluating A-I by Gauss-Jordan elimination applied to the identity matrix I or by using the Doolittle LU factorization approach described in Section 2.3.3. Since a subroutine for Doolittle LU factorization is presented in Section 1.8.2, that approach is taken here. The general algorithm for the inverse power method based on the LU factorization approach is given by Eqs. (2.62) to (2.64):
Lx' = x(k)
(2.157a)
(2.157b)
(2.157c)
A FORTRAN subroutine, subroutine invpower, for implementing the inverse power method is presented below. Program main defines the data set and prints it, calls subroutine invpower to implement the inverse power method, and prints the solution. Subroutine invpower calls subroutine lufactor and subroutine solve from Section 1.8.2 to evaluate Land U. This is indicated in subroutine invpower by including the subroutine declaration statements. The subroutines themselves must be included when subroutine invpower is to be executed. Subroutine invpower then evaluates x', y(k+I), A~~~~e' and X(k+I). Convergence of }, is checked, and the solution continues or returns. After iter iterations, an error message is printed and the solution is terminated. Program main in this section contains only the statements which are different from the statements in program main in Section 2.8.1.
