Tchebyshev Acceleration Technique for Large Scale Nonsymmetric Matrices.
Teoría de sistemas de infinitas ecuaciones lineales y programación semi-infinita.
The Analysis of k-Step Iterative Methods for Linear Systems from Summability Theory
The combination technique for a two-dimensional convection-diffusion problem with exponential layers
Convection-diffusion problems posed on the unit square and with solutions displaying exponential layers are solved using a sparse grid Galerkin finite element method with Shishkin meshes. Writing for the maximum number of mesh intervals in each coordinate direction, our “combination” method simply adds or subtracts solutions that have been computed by the Galerkin FEM on , and meshes. It is shown that the combination FEM yields (up to a factor ) the same order of accuracy in the associated...
The Contraction Number of a Multigrid Method for Solving the Poisson Equation.
The Convergence of Inexact Chebyshev and Richardson Iterative Methods for Solving Linear Systems.
The Convergence rate and Complexity of Precondotioned Iterative methods based on Approximate finite Element matrix Factorization
The convergence rate of the Chebyshev semiiterative method under a perturbation of the foci of an elliptic domain.
The descent algorithms for solving symmetric Pareto eigenvalue complementarity problem
For the symmetric Pareto Eigenvalue Complementarity Problem (EiCP), by reformulating it as a constrained optimization problem on a differentiable Rayleigh quotient function, we present a class of descent methods and prove their convergence. The main features include: using nonlinear complementarity functions (NCP functions) and Rayleigh quotient gradient as the descent direction, and determining the step size with exact linear search. In addition, these algorithms are further extended to solve the...
The extrapolated successive overrelaxation (ESOR) method for consistently ordered matrices.
The frequency decomposition multi-grid method. II. Convergence analysis based on the additive Schwarz method.
The Frequency Decomposition Multi-Grid Method. Part I: Application to Anisotropic Equations.
The Hierarchical Basis Multigrid Method.
The interplay between classical analysis and (numerical) linear algebra -- a tribute to Gene H. Golub.
The method of fictitious right-hand sides
The paper deals with the application of a fast algorithm for the solution of finite-difference systems for boundary-value problems on a standard domain (e.g. on a rectangle) to the solution of a boundary-value problem on a domain of general shape contained in the standard domain. A simple iterative procedure is suggested for the determination of fictitious right-hand sides for the system on the standard domain so that its solution is the desired one. Under the assumptions that are usual for matrices...
The Neumann-Dirichlet Domain Decomposition Method with Inexact Solvers on the Subdomains.
The new iteration methods for solving absolute value equations
Many problems in operations research, management science, and engineering fields lead to the solution of absolute value equations. In this study, we propose two new iteration methods for solving absolute value equations , where is an -matrix or strictly diagonally dominant matrix, and is an unknown solution vector. Furthermore, we discuss the convergence of the proposed two methods under suitable assumptions. Numerical experiments are given to verify the feasibility, robustness and effectiveness...
The Rate of Convergence of an Approximate Matrix Factorization Semi-Direct Method.
The Rate of Convergence of Conjugate Gradients.
The RCWA method - A case study with open questions and perspectives of algebraic computations.