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A method is proposed by which the number of transformation matrices in the product form of the inverse for the revised simple× method of solution of li~e:tr programs need never exceed the ~mmber of rows in the problem.The method is offered with t~ view to partially alleviating one of the priucipal disMvantages of the traditional product form algorithm, namely, the need for frequent re-inversions of the basis in order to reduce the number of transformations, without sacrificing too much of its advantages, such as the sparseness of the inverse and the ease with which the ittverse is kept current. The chief advantage of this proposal is that the number of nonzeros in the inverse representation is conserved and remains approximately constant after the initial buildup.

COMPUTER CODES for solving linear programs by the simplex method usually use one of three forms in representing the problem during the course of solution. These are: (a) -the standard form or original simplex method; (b) -the revised simplex method with expllcit inverse; and (c) -the revised simplex method with inverse in product form I. /~or a comparison of the relative efficiencies of the three methods, see text by Wolff and Cutler2.7 It is hoped that the method to be proposed will at least partially alleviate one of the principal disadvantages of (c), the product form algorithm, namely the need for :flnDquen% reinversion of the basis to reduce the number of transformations, without sacrificing too much of some of its advantages, such as the sparseness of the inverse and the ease with which the inverse is kept current. The chief advantage of this proposal is that the number of nonzeros in the inverse representation is conserved and remains approximately constant after the initial buildup.

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