Scaling Algorithm to Equilibrate Both Rows and Columns Norms in Matrices

摘要

The authors present an iterative procedure which asymtotically scales theinfinity norm of both rows and columns in a matrix to 1. This scaling strategy exhibits some optimality properties and additionally preserves symmetry. The algorithm also shows fast linear convergence with an asymptotic rate of one half. The authors discuss possible extensions of such an algorithm when considering the one-norm or the two norm of the rows an columns of the given matrix, and gives the proof of its convergence when the matrix pattern satisfies some common properties.