ABS Algorithms for Linear Systems and Optimization

We present a review and bibliography of the main results obtained during a research on ABS (Abaffy, Broyden, Spedicato) methods.

[1]  Victor Pereyra,et al.  Iterative methods for solving nonlinear least squares problems , 1967 .

[2]  C. G. Broyden.  On the numerical stability of Huang's update , 1989 .

[3]  Z. Li,et al.  Restarted and Truncated Versions of ABS Methods for Large Linear Systems: a Basic Framework , 1997, LSSC.

[4]  Zhijian Huang,et al.  Row update ABS methods for systems of nonlinear equations , 1994 .

[5]  S. Nicolai,et al.  A bibliography of the ABS methods , 1997 .

[6]  E. Spedicato.  A review of ABS algorithms for general linear systems , 1992 .

[7]  H. Y. Huang.  A direct method for the general solution of a system of linear equations , 1975 .

[8]  E. Bodon,et al.  ABS METHODS FOR KT EQUATIONS , 1996 .

[9]  Z. Huang.  Convergence analysis of the nonlinear block scaled ABS methods , 1992 .

[10]  K. Phua.  Solving sparse linear systems by an abs-method that corresponds toLU-decomposition , 1988 .

[11]  A. Galántai.  The global convergence of the ABS methods for a class of nonlinear problems , 1994 .

[12]  Emilio Spedicato,et al.  On some classes of iterative ABS-like methods for large-scale linear systems , 2000 .

[13]  Variationally derived algorithms in the ABS class for linear systems , 1987 .

[14]  Maria Teresa Vespucci,et al.  A bibliography on the ABS methods , 1992 .

[15]  Criteria for transforming a Z-matrix into an M-matrix , 1992 .

[16]  Frank J. Zeleznik,et al.  Quasi- Newton Methods for Nonlinear Equations , 1968, JACM.

[17]  E. Spedicato,et al.  A class of scaled direct methods for linear systems , 1990 .

[18]  Maria Teresa Vespucci,et al.  Variations on the Gram-Schmidt and the Huang algorithms for linear systems: A numerical study , 1993 .

[19]  E. Spedicato,et al.  Optimally stable ABS methods for nonlinear underdetermined systems , 1995 .

[20]  E. Spedicato.  Computer Algorithms for Solving Linear Algebraic Equations , 1991, NATO ASI Series.

[21]  Zun-Quan Xia,et al.  The implicit LX method of the ABS class , 1997 .

[22]  Xia Zun-quan,et al.  A class of descent algorithms for nonlinear function minimization with linear equality constraints , 1992 .

[23]  Variationally derived ABS methods , 1992 .

[24]  N. Deng,et al.  Further results on the local convergence of the nonlinear ABS algorithms , 1992 .

[25]  Jinxi Zhao,et al.  Explicit general solution of the Quasi-Newton equation with sparsity and symmetry , 1993 .

[26]  Zhang Liwei.  On the ABS algorithm with singular initial matrix and its application to linear programming , 1997 .

[27]  Zun-Quan Xia,et al.  Finding subgradients or descent directions of convex functions by external polyhedral approximation of subdifferentials , 1992 .

[28]  Emilio Spedicato,et al.  A class of difference ABS-type algorithms for a nonlinear system of equations , 1994, Numer. Linear Algebra Appl..

[29]  C. G. Broyden.  On the numerical stability of Huang's and related methods , 1985 .

[30]  Least change properties of ABS methods and their application in secant-type updates , 1997 .

[31]  On the ABS algorithms for perturbed linear systems , 1989 .

[32]  Zun-Quan Xia,et al.  Finding general solutions of the Quasi-Newton equation via the ABS approach , 1992 .

[33]  Aurél Galántai,et al.  Quasi-Newton ABS methods for solving nonlinear algebraic systems of equations , 1996 .

[34]  E. Spedicato,et al.  A class of direct methods for linear systems , 1984 .

[35]  Numerical experiments with the symmetric algorithm in the ABS class for linear systems , 1987 .

[36]  Zhijian Huang,et al.  An orthogonally scaled ABS method for nonlinear least squares problems , 1992 .

[37]  Emilio Spedicato,et al.  Solution of linear least squares via the ABS algorithm , 1993, Math. Program..

[38]  Anna Torriero,et al.  Sul calcolo dell'autovalore di Frobenius di matrici non negative , 1994 .