We study a perturbation-resilient iterative method with an infinite pool of operators having a property, which allows using discontinuous operators, weaker than paracontracting. A convergence result is given under an ...
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We study a perturbation-resilient iterative method with an infinite pool of operators having a property, which allows using discontinuous operators, weaker than paracontracting. A convergence result is given under an extra condition which is inherently present in some state-of-the-art iterativemethods. To evaluate the study, we develop a new algorithmic scheme which generalizes both the string-averaging algorithm and the block-iterative projection methods, and give its convergence analysis for the consistent case.
This paper formalizes a general technique to combine different methods in the solution of large systems of nonlinear equations using parallel asynchronous implementations on distributed-memory multiprocessor systems. ...
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This paper formalizes a general technique to combine different methods in the solution of large systems of nonlinear equations using parallel asynchronous implementations on distributed-memory multiprocessor systems. Such combinations of methods, referred to as Team Algorithms, are evaluated as a way of obtaining desirable properties of different methods and a sufficient condition for their convergence is derived. The load flow problem of electrical power networks is presented as an example problem that, under certain conditions, has the characteristics io make a Tearri Algorithm an appealing choice for its solution. Experimental results of an implementation on an Intel iPSC/860 Hypercube are reported, showing that considerable speedup and robustness can be obtained using team algorithms.
In this article, using three function evaluations, we discuss a nine-point compact scheme of O( triangle y(2) + triangle x(4)) based on Numerovtype discretization for the solution of 2D quasi-linear elliptic equations...
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In this article, using three function evaluations, we discuss a nine-point compact scheme of O( triangle y(2) + triangle x(4)) based on Numerovtype discretization for the solution of 2D quasi-linear elliptic equations with given Dirichlet boundary conditions, where triangle y > 0 and triangle x > 0 are grid sizes in y-and x-directions, respectively. iterativemethods for diffusion-convection equation are discussed in detail. We use blockiterativemethods to solve the system of algebraic linear and nonlinear difference equations. Comparative results of some physical problems are given to illustrate the usefulness of the proposed method.
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