balanc

Arguments

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.

Description

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

Remark

Balancing is made in the functions bdiag and spec.

Examples

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,:))

See also

• bdiag — block diagonalization, generalized eigenvectors
• spec — eigenvalues of matrices and pencils
• schur — [ordered] Schur decomposition of matrix and pencils