glever

glever — inverse of matrix pencil

Calling sequence

[Bfs,Bis,chis]=glever(E,A [,s])

`E, A`	: two real square matrices of same dimensions
`s`	: character string (default value '`s`')
`Bfs,Bis`	: two polynomial matrices
`chis`	: polynomial

Computation of

(s*E-A)^-1

by generalized Leverrier's algorithm for a matrix pencil.



(s*E-A)^-1 = (Bfs/chis) - Bis.

chis = characteristic polynomial (up to a multiplicative constant).

Bfs = numerator polynomial matrix.

Bis = polynomial matrix ( - expansion of (s*E-A)^-1 at infinity).

Note the - sign before Bis.

This function uses cleanp to simplify Bfs,Bis and chis.



s=%s;F=[-1,s,0,0;0,-1,0,0;0,0,s-2,0;0,0,0,s-1];
[Bfs,Bis,chis]=glever(F)
inv(F)-((Bfs/chis) - Bis)

F. D. (1988)