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
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 (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

SEE ALSO
glever, pencan, rowshuff

AUTHOR
F. D. (1988,1990)