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 Paperback (6"x9"), 592 pages, 60 figures ISBN 0954612078 RRP £24.95 ($39.95) |

## 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 0954612078 | GNU Scientific Library Reference Manual - Third Edition (v1.12) | See the print edition |