rowshuff

shuffle algorithm

Calling Sequence

[Ws,Fs1]=rowshuff(Fs, [alfa])

Arguments

:Fs square real pencil Fs = s*E-A : :Ws polynomial matrix : :Fs1 square real pencil F1s = s*E1 -A1 with E1 non-singular : :alfa real number ( alfa = 0 is the default value) :

Description

Shuffle algorithm: Given the pencil Fs=s*E-A, returns Ws=W(s) (square polynomial matrix) such that:

Fs1 = s*E1-A1 = W(s)*(s*E-A) is a pencil with non singular E1 matrix.

This is possible iff the pencil Fs = s*E-A is regular (i.e. invertible). The degree of Ws is equal to the index of the pencil.

The poles at infinity of Fs are put to alfa and the zeros of Ws are at alfa.

Note that (s*E-A)^-1 = (s*E1-A1)^-1 * W(s) = (W(s)*(s*E-A))^-1 *W(s)

Examples

F=`randpencil`_([],[2],[1,2,3],[]);
F=`rand`_(5,5)*F*`rand`_(5,5);   // 5 x 5 regular pencil with 3 evals at 1,2,3
[Ws,F1]=rowshuff(F,-1);
[E1,A1]=`pen2ea`_(F1);
`svd`_(E1)           //E1 non singular
`roots`_(`det`_(Ws))
`clean`_(`inv`_(F)-`inv`_(F1)*Ws,1.d-7)

See Also

• pencan canonical form of matrix pencil
• glever inverse of matrix pencil
• penlaur Laurent coefficients of matrix pencil