Scilab Home page | Wiki | Bug tracker | Forge | Mailing list archives | ATOMS | File exchange
Please login or create an account
Change language to: English - Français - Português - 日本語

Please note that the recommended version of Scilab is 6.0.0. This page might be outdated.
See the recommended documentation of this function

Справка Scilab >> Linear Algebra > Eigenvalue and Singular Value > balanc

balanc

matrix or pencil balancing

Calling Sequence

[Ab,X]=balanc(A)
[Eb,Ab,X,Y]=balanc(E,A)

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
Scilab Enterprises
Copyright (c) 2011-2017 (Scilab Enterprises)
Copyright (c) 1989-2012 (INRIA)
Copyright (c) 1989-2007 (ENPC)
with contributors
Last updated:
Thu Oct 02 14:01:04 CEST 2014