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Please note that the recommended version of Scilab is 2025.0.0. This page might be outdated.
See the recommended documentation of this function
psmall
spectral projection
Calling Sequence
[Q,M]=psmall(A,thres,flag)
Arguments
- 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 modulus < 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
.
Examples
Authors
F. Delebecque INRIA. (1988);
Used Functions
This function is based on the ordered schur form (scilab
function schur
).
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