Istituto di Scienza e Tecnologie dell'Informazione     
Arioli M., Duff I., Gould N., Reid J. Use of the P(4) and P(5) algorithms for in-core factorization of sparse matrices. In: IAM Journal on Scientific and Statistical Computing, vol. 11 (5) pp. 913 - 927. SIAM, 1990.
Variants or thc P∆4 algorithm or Hellerman and Rarick and the P∆5 algorithm or Erisman, Grimes, Lewis, and Poole, used for generating a bordered block triangular form for the in-core solution of sparse sets or linea equations, are considered. A particular concern is with maintaining numerical stability. Methods for ensuring stabilily and the extra cost that they entail are discussed. DifTerent factorization schemes are also examineel. The uses of matrix modification and iterative refinement are considered, and the best variant is compared with an established code for the solution of unsymmetric sparse sels or linear equations. The established code is usually found to be the most effective method.
Subject Sparse matrices
Linear programming
Bordered block triangular form
Gaussian elimination
Numerical stability

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