ABS algorithms for linear equations and optimization
نویسندگان
چکیده
منابع مشابه
Abs Algorithms for Linear Equations and Abspack
We present the main results obtained during a research on ABS methods in the framework of the project Analisi Numerica e Matematica Computazionale. 1. – The ABS algorithms. ABS algorithms were introduced by Abaffy, Broyden and Spedicato (1984), to solve linear equations first in the form of the basic ABS class, later generalized as the scaled ABS class and applied to linear least squares, nonli...
متن کاملABS methods for continuous and integer linear equations and optimization
ABS methods are a large class of algorithms for solving continuous and integer linear algebraic equations, and nonlinear continuous algebraic equations, with applications to optimization. Recent work by Chinese researchers led by Zunquan Xia has extended these methods also to stochastic, fuzzy and infinite systems, extensions not considered here. The work on ABS methods began almost thirty year...
متن کاملAbs Algorithms for Linear Systems and Optimization: a Review and a Bibliography
In this paper, we 1. The scaled ABS class. ABS methods have been introduced by Abaffy, Broyden and Spedicato (1984), in a paper where the solution of linear algebraic equations was considered via the so called ABS unscaled or basic class. That class was later generalized to the so called scaled ABS class and then applied also to the solution of linear least squares, nonlinear algebraic equation...
متن کاملSolving piecewise linear equations in abs-normal form
With the ultimate goal of iteratively solving piecewise smooth (PS) systems, we consider the solution of piecewise linear (PL) equations. As shown in [Gri13] PL models can be derived in the fashion of automatic or algorithmic differentiation as local approximations of PS functions with a second order error in the distance to a given reference point. The resulting PL functions are obtained quite...
متن کاملABS Solution of equations of second kind and application to the primal-dual interior point method for linear programming
Abstract We consider an application of the ABS procedure to the linear systems arising from the primal-dual interior point methods where Newton method is used to compute path to the solution. When approaching the solution the linear system, which has the form of normal equations of the second kind, becomes more and more ill conditioned. We show how the use of the Huang algorithm in the ABS cl...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2000
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(00)00419-2