A description of Winograd's new method of computing inner products and the improvement it makes possible in linear programming (LP), particularly with the revised simplex method. To price out in LP, the Winograd procedure requires half as many multiplications and about twice as many additions as the standard procedure. If multiplying takes three times as long as adding--fairly representative for current computers--the improvement is a dramatic 25 percent. Where a good starting basis is known, as often happens in Markov renewal programming, matrix inversion is about twice as fast as the usual scheme. 5 pp. Ref.
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