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pbig Scilab Group Scilab Function pbig
NAME
pbig - eigen-projection
CALLING SEQUENCE
[Q,M]=pbig(A,thres,flag)
PARAMETERS
A : real square matrix
thres : real number
flag : character string ('c' or 'd')
Q,M : real matrices
DESCRIPTION
Projection on eigen-subspace associated with eigenvalues with real part
>= thres (flag='c') or with magnitude >= thres (flag='d'). The
projection is defined by Q*M, Q is full column rank, M is full row rank
and M*Q=eye.
If flag='c', the eigenvalues of M*A*Q = eigenvalues of A with real part
>= thres.
If flag='d', the eigenvalues of M*A*Q = eigenvalues of A with magnitude
>= thres.
If flag='c' and if [Q1,M1] = full rank factorization (fullrf) of
eye()-Q*M then eigenvalues of M1*A*Q1 = eigenvalues of A with real part
< thres.
If flag='d' and if [Q1,M1] = full rank factorization (fullrf) of
eye()-Q*M then eigenvalues of M1*A*Q1 = eigenvalues of A with magnitude
< thres.
EXAMPLE
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)
SEE ALSO
psmall, projspec, fullrf
AUTHOR
F. D. (1988)
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