Man Scilab

psmall - spectral projection

Calling Sequence

[Q,M]=psmall(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 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

A=diag([1,2,3]);X=rand(A);A=inv(X)*A*X;
[Q,M]=psmall(A,2.5,'d');
spec(M*A*Q)
[Q1,M1]=fullrf(eye()-Q*M);
spec(M1*A*Q1)
 
  

See Also

pbig ,   proj ,   projspec ,  

Author

F. Delebecque INRIA. (1988);

Used Function

This function is based on the ordered schur form (scilab function schur ).

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