共查询到20条相似文献,搜索用时 15 毫秒
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Golikov A. I. Evtushenko Yu. G. Kaporin I. E. 《Computational Mathematics and Mathematical Physics》2019,59(12):2017-2032
Computational Mathematics and Mathematical Physics - A Newton-type method is proposed for numerical minimization of convex piecewise quadratic functions, and its convergence is analyzed.... 相似文献
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Zhi-Hao Cao 《计算数学(英文版)》1991,9(4):378-387
In this paper we study the polynomial acceleration methods for solving singular linear systems. We establish iterative schemes, show their convergence and find iteration error bounds. 相似文献
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A version of the Dynamical Systems Method (DSM) for solving ill-conditioned linear algebraic systems is studied in this paper. An a priori and a posteriori stopping rules are justified. An algorithm for computing the solution using a spectral decomposition of the left-hand side matrix is proposed. Numerical results show that when a spectral decomposition of the left-hand side matrix is available or not computationally expensive to obtain the new method can be considered as an alternative to the Variational Regularization. 相似文献
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本文考虑带约束的变分不等式系统.提出一个基于增广Lagrangian对偶的分解算法,本文给出了算法的收敛性分析. 相似文献
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针对反问题中出现的第一类算子方程Au=f,其中A是实Hilbert空间H上的一个无界线性算子利用动力系统方法和正则化方法,求解上述问题的正则化问题的解:u'(t)=-A~*(Au(t)-f)利用线性算子半群理论可以得到上述正则化问题的解的半群表示,并证明了当t→∞时,所得的正则化解收敛于原问题的解. 相似文献
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Border polynomial and discriminant variety are two important notions related to parametric polynomial system solving, in particular, for partitioning the parameter space into regions where the solutions of the system depend continuously on the parameter values. In this paper, we study the relations between those notions in the case of parametric triangular systems. We also investigate the properties and computation of the non-properness locus of the canonical projection restricted at a parametric regular chain or at its saturated ideal. 相似文献
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Homotopy Method for Solving Variational Inequalities 总被引:1,自引:0,他引:1
In this paper, a globally convergent method of finding solutions for an ordinary finite-dimensional variational inequality is presented by using a homotopy method. A numerical example is given to support this method. 相似文献
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B. V. Ganin A. I. Golikov Yu. G. Evtushenko 《Computational Mathematics and Mathematical Physics》2018,58(2):159-169
In order to solve an underdetermined system of linear equations with nonnegative variables, the projection of a given point onto its solutions set is sought. The dual of this problem—the problem of unconstrained maximization of a piecewise-quadratic function—is solved by Newton’s method. The problem of unconstrained optimization dual of the regularized problem of finding the projection onto the solution set of the system is considered. A connection of duality theory and Newton’s method with some known algorithms of projecting onto a standard simplex is shown. On the example of taking into account the specifics of the constraints of the transport linear programming problem, the possibility to increase the efficiency of calculating the generalized Hessian matrix is demonstrated. Some examples of numerical calculations using MATLAB are presented. 相似文献
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Stephen A. Clark 《Positivity》2006,10(3):475-489
The existence of a feasible solution to a system of infinite-dimensional linear inequalities is characterized by a topological
generalization of the Farkas Condition. If this result is specialized to a finite-dimensional vector space with finite positive
cone, then a geometric proof of the classic Minkowski-Farkas Lemma is obtained. A dual version leads to an infinite-dimensional
extension of the Theorem of the Alternative. 相似文献
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This paper is concerned with the linear approximation method (i.e. the iterative method in which a sequence of vectors is generated by solving certain linearized subproblems) for solving the variational inequality. The global convergent iterative process is proposed by applying the continuation method, and the related problems are discussed. A convergent result is obtained for the approximation iteration (i.e. the iterative method in which a sequence of vectors is generated by solving certain linearized subproblems approximately). 相似文献
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用遗传算法求解病态线性方程组 总被引:15,自引:0,他引:15
众所周知 ,病态方程组的条件数较大 ,当输入数据有微小扰动或计算过程中的舍入误差都可能引起输出数据的很大扰动 ,使得解严重失真 ,因此求解此类方程组是相当困难的 .本文尝试使用遗传算法来求解病态线性方程组 ,得到了较好的结果 ,并与传统的求解方法作了简单的比较 相似文献
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In this paper,we present a generalized Newton-like method for solving variational inequalities,and prove Q-superlinear and Q-quadratic convergence without the strict complementarity slackness condition 相似文献