Scilab Website | Contribute with GitLab | Mailing list archives | ATOMS toolboxes
Scilab Online Help
6.0.0 - Русский

Change language to:
English - Français - 日本語 - Português -

Please note that the recommended version of Scilab is 2024.0.0. This page might be outdated.
See the recommended documentation of this function

Справка Scilab >> Linear Algebra > Matrix Pencil > penlaur

penlaur

Laurent coefficients of matrix pencil

Syntax

[Si,Pi,Di,order]=penlaur(Fs)
[Si,Pi,Di,order]=penlaur(E,A)

Arguments

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)

See also

  • glever — inverse of matrix pencil
  • pencan — canonical form of matrix pencil
  • rowshuff — shuffle algorithm
Report an issue
<< pencan Matrix Pencil quaskro >>

Copyright (c) 2022-2023 (Dassault Systèmes)
Copyright (c) 2017-2022 (ESI Group)
Copyright (c) 2011-2017 (Scilab Enterprises)
Copyright (c) 1989-2012 (INRIA)
Copyright (c) 1989-2007 (ENPC)
with contributors
Last updated:
Tue Feb 14 15:13:21 CET 2017