1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
|
.TH penlaur 1 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
penlaur - Laurent coefficients of matrix pencil
.SH CALLING SEQUENCE
.nf
[Si,Pi,Di,order]=penlaur(Fs)
[Si,Pi,Di,order]=penlaur(E,A)
.fi
.SH PARAMETERS
.TP 12
Fs
: a regular pencil \fVs*E-A\fR
.TP 12
E, A
: two real square matrices
.TP 12
Si,Pi,Di
: three real square matrices
.TP
order
: integer
.SH DESCRIPTION
.Vb penlaur
computes the first Laurent coefficients of \fV(s*E-A)^-1\fR at
infinity.
.LP
\fV(s*E-A)^-1 = ... + Si/s - Pi - s*Di + ...\fR at \fVs\fR = infinity.
.LP
\fVorder\fR = order of the singularity (order=index-1).
.LP
The matrix pencil \fVFs=s*E-A\fR should be invertible.
.LP
For a index-zero pencil, \fVPi, Di,...\fR are zero and \fVSi=inv(E)\fR.
.LP
For a index-one pencil (order=0),\fVDi\fR =0.
.LP
For higher-index pencils, the terms \fV -s^2 Di(2), -s^3 Di(3),... \fR are given by:
.LP
\fV Di(2)=Di*A*Di\fR, \fV Di(3)=Di*A*Di*A*Di \fR (up to \fVDi(order)\fR).
.SH Remark
Experimental version: troubles when bad conditioning of \fVso*E-A\fR
.SH EXAMPLE
.nf
F=randpencil([],[1,2],[1,2,3],[]);
F=rand(6,6)*F*rand(6,6);[E,A]=pen2ea(F);
[Si,Pi,Di]=penlaur(F);
[Bfs,Bis,chis]=glever(F);
norm(coeff(Bis,1)-Di,1)
.fi
.SH SEE ALSO
glever, pencan, rowshuff
.SH AUTHOR
F. D. (1988,1990)
|
