penlaur

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

Examples



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)

Author

F. Delebecque INRIA(1988,1990) ;