作者：
Ge, Ren-DongXia, Zun-QuanCORA
Department of Applied Mathematics Dalian University of Technology Dalian 116024 China
A modified discretization abs algorithm for solving a class of singular nonlinear systems, F(x) = 0, where x, F ε Rn, is presented, constructed by combining a discretization abs algorithm and a method of Hoy and Schw...
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A modified discretization abs algorithm for solving a class of singular nonlinear systems, F(x) = 0, where x, F ε Rn, is presented, constructed by combining a discretization abs algorithm and a method of Hoy and Schwetlick (1990). The second order differential operation of F at a point is not required to be calculated directly in this algorithm. Q-quadratic convergence of this algorithm is given.
In this paper the abs algorithm with singular initial matrix is considered and used to construct an active set algorithm for solving the linear programming problem. We prove that this active set algorithm is reduced t...
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In this paper the abs algorithm with singular initial matrix is considered and used to construct an active set algorithm for solving the linear programming problem. We prove that this active set algorithm is reduced to the simplex algorithm when it starts from a vertex or it meets a vertex.
The abs class for linear and nonlinear systems has been recently introduced by Abaffy, Broyden, Galantai and Spedicato. Here we consider various ways of applying these algorithms to the determination of the minimal eu...
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The abs class for linear and nonlinear systems has been recently introduced by Abaffy, Broyden, Galantai and Spedicato. Here we consider various ways of applying these algorithms to the determination of the minimal euclidean norm solution of over-determined linear systems in the least squares sense. Extensive numerical experiments show that the proposed algorithms are efficient and that one of them usually gives better accuracy than standard implementations of the QR orthogonalization algorithm with Householder reflections.
This paper studies the minimum norm correction methods for solving a linear system of equations which can be viewed as an extension to [3]. The minimum norm class of algorthims and its properties are studied. Furtherm...
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Using a strict bound of Spedicato to the condition number of bordered positive-definite matrices, we show that the scaling parameter in the abs class for linear systems can always be chosen so that the bound of a cert...
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Using a strict bound of Spedicato to the condition number of bordered positive-definite matrices, we show that the scaling parameter in the abs class for linear systems can always be chosen so that the bound of a certain update matrix is globally minimized. Moreover, if the scaling parameter is so chosen at every iteration, then the condition number itself is globally minimized. The resulting class of optimally conditioned algorithms contains as a special case the class of optimally stable algorithms in the sense of Broyden.
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