1,720,979 research outputs found
A modulus-based nonsmooth Newton’s method for solving horizontal linear complementarity problems
No full textA nonlinearity lagging method for non-steady diffusion equations with nonlinear convection terms
Full text linkWe analyze an iterative procedure for solving nonlinear algebraic systems arising from the discretization of nonlinear, non-steady reaction-convection-diffusion equations with non-constant (and, in general, nonlinear) velocity terms. The basic idea underlying the procedure consists in lagging the diffusion and the velocity terms of the discretized system, which is thus partly linearized. After analyzing the discretized system and proving some results on the monotonicity of the operators and on the uniqueness of the solution, we prove sufficient conditions that ensure the convergence of this lagged method. We also describe the inner iteration and show how the weakly nonlinear systems arising at each lagged iteration can be solved efficiently. Finally, we analyze numerically the entire solution process by several numerical experiments
Implementation of Splitting Method for Solving Block Tridiagonal Linear Systems on Transputers
No full textModulus-based matrix splitting algorithms for generalized complex-valued horizontal linear complementarity problems
Full text linkIn this paper, we introduce the complex-valued horizontal linear complementarity problem (CHLCP), we provide two equivalent real-valued reformulations, and study modulus-based matrix splitting algorithms for solving the CHLCP. This latter point is motivated by the recent introduction of modulus-based matrix splitting methods for (non-horizontal) complex linear complementarity problems (CLCPs), which we generalize. We study the convergence of the proposed algorithms. Whenever possible, we seek convergence conditions that are directly based on the form of the real and imaginary parts of the matrices of the CHLCP in its complex form. This makes the convergence easier to evaluate than in existing convergence analyses. Finally, we study the numerical properties of the proposed algorithms by solving several CHLCPs. In this context, we also revisit results on the CLCP under the larger CHLCP framework, providing new numerical insights on the efficiency of existing algorithms for the CLCP
Splitting methods for constrained quadratic programs in data analysis
No full textThis paper is concerned with the numerical solution of a linearly constrained quadratic programming problem by methods that use a splitting of the objective matrix. We present an acceleration step for a general splitting algorithm and we establish the convergence of the resulting accelerated scheme. We report the results of numerical experiments arising in constrained bivariate interpolation to evaluate the efficiency of this acceleration technique for a particular splitting of the objective matrix and for the corresponding extrapolated form
An iterative method for large sparse linear systems on a vector computer
No full textIn this paper we consider the arithmetic mean method for solving large sparse systems of linear equations. This iterative method converges for systems with coefficient matrices that are symmetric positive definite or positive real or irreducible L-matrices with a strong diagonal dominance. The method is very suitable for parallel implementation on a multiprocessor system, such as the CRAY X-MP. Some numerical experiments on systems resulting from the discretization, by means of the usual 5-point difference formulae, of an elliptic partial differential equation are presented
Splitting methods for quadratic optimization in data analysis
No full textMany problems arising in data analysis can be formulated as a large sparse strictly convex quadratic programming problems with equality and inequality linear constraints. In order to solve these problems, we propose an iterative scheme based on a splitting of the matrix of the objective function and called splitting algorithm (SA). This algorithm transforms the original problem into a sequence of subproblems easier to solve, for which there exists a large number of efficient methods in literature. Each subproblem can be solved as a linear complementarity problem or as a constrained least distance problem. We give conditions for SA convergence and we present an application on a large scale sparse problem arising in constrained bivariate interpolation. In this application we use a special version of SA called diagonalization algorithm (DA). An extensive experimentation on CRAY C90 permits to evaluate the DA performance
A minimization method for the solution of large symmetric eigenproblems
No full textThis paper concerns with the solution of a special eigenvalue problem for a large sparse symmetric matrix by a fast convergent minimization method. A theoretical analysis of the
method is developed; it is proved that is convergent with a convergence rate of fourth order. This minimization method requires to solve a sequence of equality-constrained least squares problems that become increasingly ill-conditioned, as the solution of eigenvalue problem is approached. A particular attention has been addressed to this question of ill-conditioning for the practical application of the method. Computational experiments carried out on Cray C90 show the behaviour of this minimization method as accelerating technique of the inverse iteration method. Also a comparison with the scaled Newton method has been done
A generalization of the equivalence relations between modulus-based and projected splitting methods
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