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.TH quaskro 1 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
quaskro - quasi-Kronecker form
.SH CALLING SEQUENCE
.nf
[Q,Z,Qd,Zd,numbeps,numbeta]=quaskro(F)
[Q,Z,Qd,Zd,numbeps,numbeta]=quaskro(E,A)
[Q,Z,Qd,Zd,numbeps,numbeta]=quaskro(F,tol)
[Q,Z,Qd,Zd,numbeps,numbeta]=quaskro(E,A,tol)
.fi
.SH PARAMETERS
.TP
F
: real matrix pencil \fVF=s*E-A\fR (\fVs=poly(0,'s')\fR)
.TP
E,A
: two real matrices of same dimensions
.TP
tol
: a real number (tolerance, default value=1.d-10)
.TP 10
Q,Z
:
two square orthogonal matrices
.TP
Qd,Zd
:
two vectors of integers
.TP 15
numbeps
:
vector of integers
.SH DESCRIPTION
Quasi-Kronecker form of matrix pencil: \fVquaskro\fR computes two
orthogonal matrices \fVQ, Z\fR which put the pencil \fVF=s*E -A\fR into
upper-triangular form:
.nf
| sE(eps)-A(eps) | X | X |
|----------------|----------------|------------|
| O | sE(inf)-A(inf) | X |
Q(sE-A)Z = |=================================|============|
| | |
| O | sE(r)-A(r) |
.fi
The dimensions of the blocks are given by:
.PP
\fVeps=Qd(1) x Zd(1)\fR, \fVinf=Qd(2) x Zd(2)\fR,
\fVr = Qd(3) x Zd(3)\fR
.LP
The \fVinf\fR block contains the infinite modes of
the pencil.
.LP
The \fVf\fR block contains the finite modes of
the pencil
.LP
The structure of epsilon blocks are given by:
.PP
\fVnumbeps(1)\fR = # of eps blocks of size 0 x 1
.PP
\fVnumbeps(2)\fR = # of eps blocks of size 1 x 2
.PP
\fVnumbeps(3)\fR = # of eps blocks of size 2 x 3 etc...
.LP
The complete (four blocks) Kronecker form is given by
the function \fVkroneck\fR which calls \fVquaskro\fR on
the (pertransposed) pencil \fVsE(r)-A(r)\fR.
.LP
The code is taken from T. Beelen
.SH SEE ALSO
kroneck, gschur, gspec
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