matrix or pencil balancing
[Ab,X]=balanc(A)
[Eb,Ab,X,Y]=balanc(E,A)
| A: | a real square matrix |
|---|
: :X: a real square invertible matrix : :E: a real square matrix (same dimension as A) : :Y: a real square invertible matrix. :
Balance a square matrix to improve its condition number.
[Ab,X] = balanc(A) finds a similarity transformation X such that
Ab = inv(X)*A*X has approximately equal row and column norms.
For matrix pencils,balancing is done for improving the generalized eigenvalue problem.
[Eb,Ab,X,Y] = balanc(E,A) returns left and right transformations X and Y such that Eb=inv(X)*E*Y, Ab=inv(X)*A*Y
Balancing is made in the functions bdiag and spec.
A=[1/2^10,1/2^10;2^10,2^10];
[Ab,X]=balanc(A);
`norm`_(A(1,:))/`norm`_(A(2,:))
`norm`_(Ab(1,:))/`norm`_(Ab(2,:))