On the Gauss, Cholesky and Householder algorithms

Householder, 1964 Gastinel, 1966 Ciarlet, 1980 Durand, 1972, Solutions Numériques des Equations Algébriques., Tome II, Masson et cie Rotella, 1995, Théorie et Pratique du Calcul Matriciel, Éditions Technip Golub, 1989 Jennings, 1980 Minoux, 1983 Strang, 1990 Lascaux, 1993 Chatzman, 1991 Wilkinson, 1965 Benhamadou M. Développement d’Outils en Programmation Linéaire et Analyse Numérique Matricielle. Thèse No1955, de l’Université Paul Sabatier, Toulouse 3, Toulouse, France; 1994. Benhamadou, 2000, A new method to solve large linear systems: the algorithm of “recursive reduction”, Adv Eng Softw, 31, 481, 10.1016/S0965-9978(99)00064-2 Benhamadou, 2002, On the simplex algorithm revised form, Adv Eng Softw, 33, 469, 10.1016/S0965-9978(02)00037-6 Benhamadou, 2005, A new algorithm to solve nonlinear systems, Adv Eng Softw, 36, 385, 10.1016/j.advengsoft.2005.01.004 Benhamadou, 2007, Preconditioners for the resolution of the linear systems Ax=b, Appl Math Comput, 189, 927 Axelsson, 1972, A generalised SSOR method, BIT V, 13 Evans, 1967, The use of preconditioning in iterative method for solving linear equations with symmetric positive definite matrices, J Inst Math Appl, 4 Meijerink, 1977, An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix, Math Comput, 31 Chow, Edmont, Saad, Yousef. Approximate inverse preconditioners for general sparse matrices, Department of Computer Science, and Minnesota Supercomputer Institute, University of Minnesota, Mai; 1994. Congrove, 1992, Approximate inverse preconditioning for sparse linear systems, Int J Comput Math, 44, 91, 10.1080/00207169208804097 Huckle, T, Grote, M. A new approach to parallel preconditioning with sparse approximate inverses. Manuscript SCCM-94-03. Scientific computing and computational mathematics program, Stanford University Stanford, California; 1994. Huckle, T, Grote, M. Effective parallel preconditioning with sparse approximate inverses. Manuscript SCCM-94-03. Scientific computing and computational mathematics program, Stanford University Stanford, California; 1999. Tang, 1998, Toward an effective sparse approximate inverse preconditioner, SIAM J Matrix Anal Appl, 20, 970, 10.1137/S0895479897320071