First, this paper presents the results of experiments with algorithmic techniques for efficiently solving medium and large scale linear and mixed integer programming problems. The techniques presented here are either ...
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First, this paper presents the results of experiments with algorithmic techniques for efficiently solving medium and large scale linear and mixed integer programming problems. The techniques presented here are either original or recent. The solution of a great number of problems has shown that efficient problem solving requires automatic adaptation of algorithmic techniques upon problem characteristics. We show when a given technique should be used for a particular problem. The last part of this paper describes an attempt to provide a powerful mathematical programming language, allowing an easy programming of specific studies on medium-size models such as the recursive use of LP or the build-up of algorithms based on the simplex method. All these features have been implemented in the IBM Mathematical Programming System, MPSX/370, and its feature MIP/370. Extensive numerical results and comparisons on real-life problems are provided and commented upon.
It is suggested that it is almost impossible to compare two sensible implementations of a numerical algorithm in Fortran or in Algol and assert that one of them will lead to a more efficient program in machine languag...
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An algorithm is presented to compute a triangular factorization and the inertia of a symmetric matrix. The algorithm is stable even when the matrix is not positive definite and is as fast as Cholesky. Programs for sol...
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An algorithm is presented to compute a triangular factorization and the inertia of a symmetric matrix. The algorithm is stable even when the matrix is not positive definite and is as fast as Cholesky. Programs for solving associated systems of linear equations are included.
A recursive algorithm for computing the inverse of a matrix from the LU factors based on relationships in Takahashi, et al., is examined. The formulas for the algorithm are given; the dependency relationships are deri...
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A recursive algorithm for computing the inverse of a matrix from the LU factors based on relationships in Takahashi, et al., is examined. The formulas for the algorithm are given; the dependency relationships are derived; the computational costs are developed; and some general comments on application and stability are made.
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