A Scaling Algorithm to Equilibrate Both Rows and Columns Norms in Matrices 1
نویسنده
چکیده
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.
منابع مشابه
A scaling algorithm to equilibrate both rows and columns norms in matrices
Scaling or equilibration of data in linear systems of equations is a topic of great importance that has already been the subject of many scientific publications, with many different developments depending on the properties one wants to obtain after scaling. It has given rise to several well known algorithms (see Duff, Erisman, and Reid (1986), Schneider and Zenios (1990), for instance). Scaling...
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