Optimal Block Diagonal $l_2 $-Scaling of Matrices
Alexander Shapiro · SIAM Journal on Numerical Analysis · 1985
This paper is concerned with optimal one-sided and two-sided scaling of a matrix with respect to the class of block diagonal matrices. Optimality conditions are presented. A series of lower bounds for the symmetric scaling problems is introduced. Then for some special cases the solutions are given in a closed form. Finally differentiability of the best condition number as a function of a symmetric matrix is discussed.