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balanc(2) Scilab Function balanc(2)
NAME
balanc - matrix or pencil balancing
CALLING SEQUENCE
[Ab,X]=balanc(A)
[Eb,Ab,X,Y]=balanc(E,A)
PARAMETERS
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 eigen-
value problem.
[Eb,Ab,X,Y] = balanc(E,A) returns left and right transformations X and Y
such that Eb=X*E*Y Ab=X*A*Y
Remark
Balancing is made in the functions bdiag and spec.
EXAMPLE
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
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