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.TH balanc 2 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
balanc - matrix or pencil balancing
.SH CALLING SEQUENCE
.nf
[Ab,X]=balanc(A)
[Eb,Ab,X,Y]=balanc(E,A)
.fi
.SH PARAMETERS
.TP 10
A:
a real square matrix
.TP
X:
a real square invertible matrix
.TP
E:
a real square matrix (same dimension as \fVA\fR)
.TP
Y:
a real square invertible matrix.
.SH DESCRIPTION
Balance a square matrix to improve its condition number.
.LP
.Vb [Ab,X] = balanc(A)
finds a similarity transformation \fVX\fR such that
.Vb Ab = inv(X)*A*X
has approximately equal row and column norms.
.LP
For matrix pencils,balancing is done for improving the
generalized eigenvalue problem.
.LP
.Vb [Eb,Ab,X,Y] = balanc(E,A)
returns left and right transformations \fVX\fR and \fVY\fR
such that
.Vb Eb=X*E*Y Ab=X*A*Y
.SH Remark
Balancing is made in the functions \fVbdiag\fR and \fVspec\fR.
.SH EXAMPLE
.nf
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,:))
.fi
.SH SEE ALSO
bdiag
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