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A comparative study of algorithms for matrix balancing. (English) Zbl 0703.90094
Summary: The problem of adjusting the entries of a large matrix to satisfy prior consistency requirements occurs in economics, urban planning, statistics, demography, and stochastic modeling; these problems are called matrix balancing problems. We describe five applications of matrix balancing and compare the algorithmic and computational performance of balancing procedures that represent the two primary approaches for matrix balancing - matrix scaling and nonlinear optimization. The algorithms we study are the RAS algorithm, a diagonal similarity scaling algorithm, and a truncated Newton algorithm for network optimization. We present results from computational experiments with large-scale problems based on producing consistent estimates of Social Accounting Matrices for developing countries.

90C90 Applications of mathematical programming
15A12 Conditioning of matrices
65F35 Numerical computation of matrix norms, conditioning, scaling
90C30 Nonlinear programming
90-08 Computational methods for problems pertaining to operations research and mathematical programming
90C06 Large-scale problems in mathematical programming
90C35 Programming involving graphs or networks
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