Strong Underrelaxation in Kaczmarz's Method for Inconsistent Systems
Strong Uniqueness. A Far-Reaching Criterion for the Convergence Analysis of Iterative Procedures.
Subdirect sums of doubly diagonally dominant matrices.
Subdirect sums of -strictly diagonally dominant matrices.
Superlinear CG convergence for special right-hand sides.
Sweeping preconditioners for elastic wave propagation with spectral element methods
We present a parallel preconditioning method for the iterative solution of the time-harmonic elastic wave equation which makes use of higher-order spectral elements to reduce pollution error. In particular, the method leverages perfectly matched layer boundary conditions to efficiently approximate the Schur complement matrices of a block LDLT factorization. Both sequential and parallel versions of the algorithm are discussed and results for large-scale problems from exploration geophysics are presented....
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.