Matrix balancing
J. Grad · The Computer Journal · 1971
In this paper we prove the convergence of the sequence of similarity transformations performed on a general real matrix of order n that transform the original matrix into a balanced form where for each i from 1 to n the sums of the absolute values of elements of row i and column i are equal. For some matrices the eigenvalues computed from balanced or nearly balanced form appear to be more accurate than the eigenvalues computed from the original non-balanced matrix.