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
|
penlaur(1) Scilab Function penlaur(1)
NAME
penlaur - Laurent coefficients of matrix pencil
CALLING SEQUENCE
[Si,Pi,Di,order]=penlaur(Fs)
[Si,Pi,Di,order]=penlaur(E,A)
PARAMETERS
Fs : a regular pencil s*E-A
E, A : two real square matrices
Si,Pi,Di : three real square matrices
order : integer
DESCRIPTION
penlaur computes the first Laurent coefficients of (s*E-A)^-1 at infinity.
(s*E-A)^-1 = ... + Si/s - Pi - s*Di + ... at s = infinity.
order = order of the singularity (order=index-1).
The matrix pencil Fs=s*E-A should be invertible.
For a index-zero pencil, Pi, Di,... are zero and Si=inv(E).
For a index-one pencil (order=0),Di =0.
For higher-index pencils, the terms -s^2 Di(2), -s^3 Di(3),... are given
by:
Di(2)=Di*A*Di, Di(3)=Di*A*Di*A*Di (up to Di(order)).
Remark
Experimental version: troubles when bad conditioning of so*E-A
EXAMPLE
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)
SEE ALSO
glever, pencan, rowshuff
AUTHOR
F. D. (1988,1990)
|
