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GNU Scientific Library Reference Manual - Third Edition (v1.12)
by M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, P. Alken, M. Booth, F. Rossi
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ISBN 0954612078
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13.14 Balancing

The process of balancing a matrix applies similarity transformations to make the rows and columns have comparable norms. This is useful, for example, to reduce roundoff errors in the solution of eigenvalue problems. Balancing a matrix A consists of replacing A with a similar matrix

A' = D^(-1) A D

where D is a diagonal matrix whose entries are powers of the floating point radix.

Function: int gsl_linalg_balance_matrix (gsl_matrix * A, gsl_vector * D)
This function replaces the matrix A with its balanced counterpart and stores the diagonal elements of the similarity transformation into the vector D.
ISBN 0954612078GNU Scientific Library Reference Manual - Third Edition (v1.12)See the print edition