Applications of shortest path algorithms to matrix scalings |
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| Authors: | M v Golitschek H Schneider |
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| Institution: | (1) Institut für Angewandte Mathematik und Statistik, D-8700 Würzburg (Fed. Rep.);(2) Department of Mathematics, University of Wisconsin, 53706 Madison, Wisconsin, USA |
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| Abstract: | Summary A symmetric scaling of a nonnegative, square matrixA is a matrixXAX
–1, whereX is a nonsingular, nonnegative diagonal matrix. By associating a family of weighted directed graphs with the matrixA we are able to adapt the shortest path algorithms to compute an optimal scaling ofA, where we call a symmetric scalingA ofA optimal if it minimizes the maximum of the ratio of non-zero elements.Dedicated to Professor F.L. Bauer on the occasion of his 60th birthdayThe first author was partially supported by the Deutsche Forschungsgemeinschaft under grant GO 270/3, the second author by the U.S. National Science Foundation under grand MCS-8026132 |
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| Keywords: | AMS(MOS): 65F35 CR: 5 14 |
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