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.TH pbig 1 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
pbig - eigen-projection
.SH CALLING SEQUENCE
.nf
[Q,M]=pbig(A,thres,flag)
.fi
.SH PARAMETERS
.TP 12
A
: real square matrix
.TP 12
thres
: real number
.TP 12
flag
: character string (\fV'c'\fR or \fV'd'\fR)
.TP
Q,M
: real matrices
.SH DESCRIPTION
Projection on eigen-subspace associated with eigenvalues
with real part >= \fVthres\fR (\fVflag='c'\fR) or with
magnitude >= \fVthres\fR (\fVflag='d'\fR).
The projection is defined by \fVQ*M\fR, \fVQ\fR is full column rank,
\fVM\fR is full row rank and \fVM*Q=eye\fR.
.LP
If \fVflag='c'\fR, the eigenvalues of \fVM*A*Q\fR = eigenvalues
of \fVA\fR with real part >= \fVthres\fR.
.LP
If \fVflag='d'\fR, the eigenvalues of \fVM*A*Q\fR = eigenvalues
of \fVA\fR with magnitude >= \fVthres\fR.
.PP
If \fVflag='c'\fR and if \fV[Q1,M1]\fR = full rank factorization (\fVfullrf\fR)
of \fVeye-Q*M\fR then eigenvalues of \fVM1*A*Q1\fR = eigenvalues of \fVA\fR
with real part < \fVthres\fR.
.LP
If \fVflag='d'\fR and if \fV[Q1,M1]\fR = full rank factorization (\fVfullrf\fR)
of \fVeye-Q*M\fR then eigenvalues of \fVM1*A*Q1\fR = eigenvalues of \fVA\fR
with magnitude < \fVthres\fR.
.SH EXAMPLE
.nf
A=diag([1,2,3]);X=rand(A);A=inv(X)*A*X;
[Q,M]=pbig(A,1.5,'d');
spec(M*A*Q)
[Q1,M1]=fullrf(eye-Q*M);
spec(M1*A*Q1)
.fi
.SH SEE ALSO
psmall, projspec, fullrf
.SH AUTHOR
F. D. (1988)
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