A Scaling Algorithm to Equilibrate Both Rows and Columns Norms in Matrices 1

We present an iterative procedure which asymptotically scales the infinity 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 1=2. We discuss possible extensions of such an algorithm when considering the one-norm or the two norm of the rows and columns of the given matrix, and give the proof of its convergence when the matrix pattern satisfies some common properties.

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