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.TH glever 1 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
glever - inverse of matrix pencil
.SH CALLING SEQUENCE
.nf
[Bfs,Bis,chis]=glever(E,A [,s])
.fi
.SH PARAMETERS
.TP 12
E, A
: two real square matrices of same dimensions
.TP
s
: character string (default value '\fVs\fR')
.TP
Bfs,Bis
: two polynomial matrices
.TP
chis
: polynomial
.SH DESCRIPTION
Computation of
.IG
(s*E-A)^-1
.FI
.LA $(sE-A)^{-1} $
by generalized Leverrier's algorithm for a matrix pencil.
.nf
(s*E-A)^-1 = (Bfs/chis) - Bis.
.fi
\fVchis\fR = characteristic polynomial (up to a multiplicative constant).
.LP
\fVBfs\fR = numerator polynomial matrix.
.LP
\fVBis\fR
= polynomial matrix ( - expansion of \fV(s*E-A)^-1\fR at infinity).
.LP
Note the - sign before \fVBis\fR.
.SH Caution
This function uses \fVcleanp\fR to simplify \fVBfs,Bis\fR and \fVchis\fR.
.SH EXAMPLE
.nf
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)
.fi
.SH AUTHOR
F. D. (1988)
.SH SEE ALSO
rowshuff, det, invr, coffg, pencan, penlaur
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