Related papers: Iteration Procedure for the N-Dimensional System o…
In this paper, we introduce a new iterative method which we call one step back approach: the main idea is to anticipate the consequence of the iterative computation per coordinate and to optimize on the choice of the sequence of the…
The main purpose of this paper is providing a simple method to generate the matrices of irreducible representations because it is useful to reduce the computational time of solving the eigenvalue problems. The only information we need to…
This work wishes to support various mathematical issues concerning the iterative methods with the help of new programming languages. We consider a way to show how problems in math have an answer by using different academic resources and…
In this paper, a novel multigrid method based on Newton iteration is proposed to solve nonlinear eigenvalue problems. Instead of handling the eigenvalue $\lambda$ and eigenfunction $u$ separately, we treat the eigenpair $(\lambda, u)$ as…
A linearizable version of multidimensional system of $n$-wave type nonlinear PDEs is proposed. This system is derived using the spectral representation of its solution via the procedure similar to the dressing method for the ISTM-integrable…
A method based on order completion for solving general equations is presented. In particular, this method can be used for solving large classes of nonlinear systems of PDEs, with possibly associated initial and/or boundary value problems.
A symbolic computational algorithm which detects " linear "` solutions of nonlinear polynomial differential equations of single functions, is developed throughout this paper.
This paper presents an iterative method suitable for inverting semilinear problems which are important kernels in many numerical applications. The primary idea is to employ a parametrization that is able to reduce semilinear problems into…
We apply the monotone domain decomposition iterative method to a nonlinear integro-differential equation of Volterra type and prove its convergence. To do this, by adding a term in both sides of the original equation we make a linear…
A method of representation of a solution as segments of the series in powers of the step of the independent variable is expanded for solving complex systems of ordinary differential equations (ODE): the Lorenz system and other systems. A…
In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…
Several recent works have developed a new, probabilistic interpretation for numerical algorithms solving linear systems in which the solution is inferred in a Bayesian framework, either directly or by inferring the unknown action of the…
We investigate the use of piecewise linear systems, whose coefficient matrix is a piecewise constant function of the solution itself. Such systems arise, for example, from the numerical solution of linear complementarity problems and in the…
We introduce a new technique for solving uni-parametric versions of linear programs, convex quadratic programs, and linear complementarity problems in which a single parameter is permitted to be present in any of the input data. We…
In geometry processing, numerical optimization methods often involve solving sparse linear systems of equations. These linear systems have a structure that strongly resembles to adjacency graphs of the underlying mesh. We observe how…
We propose a novel iterative algorithm for solving a large sparse linear system. The method is based on the EM algorithm. If the system has a unique solution, the algorithm guarantees convergence with a geometric rate. Otherwise,…
We introduce a numerical method for the numerical solution of the so-called Lur'e matrix equations that arise in balancing-related model reduction and linear-quadratic infinite time horizon optimal control. Based on the fact that the set of…
A numerical method to solve linear integro-differential equations is presented. This method has been used to solve the QCD Altarelli-Parisi evolution equations within the H1 Collaboration at DESY-Hamburg. Mathematical aspects and numerical…
The problem of iterated partial summations is solved for some discrete distributions defined on discrete supports. The power method, usually used as a computational approach to finding matrix eigenvalues and eigenvectors, is in some cases…
We develop a one step matrix method in order to obtain approximate solutions of first order systems and non-linear ordinary differential equations, reducible to first order systems. We find a sequence of such solutions that converge to the…