Retooling the method of block conjugate gradients.
Robust domain decomposition preconditioners for abstract symmetric positive definite bilinear forms
An abstract framework for constructing stable decompositions of the spaces corresponding to general symmetric positive definite problems into “local” subspaces and a global “coarse” space is developed. Particular applications of this abstract framework include practically important problems in porous media applications such as: the scalar elliptic (pressure) equation and the stream function formulation of its mixed form, Stokes’ and Brinkman’s equations. The constant in the corresponding abstract...
Robust domain decomposition preconditioners for abstract symmetric positive definite bilinear forms
An abstract framework for constructing stable decompositions of the spaces corresponding to general symmetric positive definite problems into “local” subspaces and a global “coarse” space is developed. Particular applications of this abstract framework include practically important problems in porous media applications such as: the scalar elliptic (pressure) equation and the stream function formulation of its mixed form, Stokes’ and Brinkman’s equations....
Robustness of multi-grid applied to anisotropic equations on convex domains with re-entrant corners.
Round-Off Error Analysis of Iterations for Large Linear Systems.
Round-off error analysis of the gradient method
Scalable algebraic multigrid on 3500 processors.
Schwarz alternating and iterative refinemnt methods for mixed formulations of elliptic problems, part I: algorithms and numerical results.
Schwarz alternating and iterative refinemnt methods for mixed formulations of elliptic problems, part II: convergence theory.
Schwarz methods over the course of time.
Schwarz-like methods for approximate solving cooperative systems
The aim of this contribution is to propose and analyze some computational means to approximate solving mathematical problems appearing in some recent studies devoted to biological and chemical networks.
Semicoarsening multigrid for systems.
Semi-convergence and relaxation parameters for a class of SIRT algorithms.
Simple square smoothing regularization operators.
Simpler block GMRES for nonsymmetric systems with multiple right-hand sides.
Solution of system of linear equations with large coefficients in the diagonal
Solving systems of two–sided (max, min)–linear equations
A finite iteration method for solving systems of (max, min)-linear equations is presented. The systems have variables on both sides of the equations. The algorithm has polynomial complexity and may be extended to wider classes of equations with a similar structure.
Some algebraic aspects of multigrid methods
Some comparison theorems for nonnegative splittings of matrices.
Some comparisons of difference schemes on meshes of Shishkin and Bakhvalov type.