Estimating the entries of a large matrix to satisfy a set of internal consistency relations is a problem with several applications in economics, urban and regional planning, transportation, statistics and other areas. It is known as the Matrix Balancing Problem. Matrix balancing applications arising from the estimation of telecommunication or transportation traffic and from multi-regional trade flows give rise to huge optimization problems. In this report, the authors show that the RAS algorithm can be specialized for vector and parallel computing and used for the solution of very large problems. The algorithm is specialized for vector computations on a CRAY X-MP and is parallelized on an Alliant FX/8. A variant of the algorithm-developed here for its potential parallelism-turns out to be more efficient than the original algorithm even when implemented serially. The authors use the algorithms to estimate disaggregated input/output tables and a multi-regional trade flow table of the U.S. The larger problem solved has approximately 12000 constraints and over 370000 nonlinear variables. This is the first of two papers that aim at the solution of very large matrix balancing problems.
