Algorithm 348: matrix scaling by integer programming [F1]
RICHARD R. KLIMPEL · Communications of the ACM · 1969
a, m, n, g, u, v); value m, n, g; integer m, n; real g; real array a; integer array u, v; comment The use of scaling to precondition matrices so as to improve subsequent computational characteristics is of considerable importance.To measure the scaling condition of a matrix, alj (i=1, ... , m and j=l, ... , n), Fulkerson and Wolfe [1] suggested the ratio of the matrix entry of largest absolute value to that of the smallest nonzero absolute value.This procedure implements the method of [1], i.e. finding multiplicative row factors, r~, and column factors, sy, which, when applied, minimize the above condition number.The minimization problem can be expressed as an equivalent additive discrete problem by taking logarithms and defining: