Forward Error Analysis of Gaussian Elimination. Part I: Error and Residual Estimates.
Frequency analysis of preconditioned waveform relaxation iterations
The error analysis of preconditioned waveform relaxation iterations for differential systems is presented. This analysis extends and refines previous results by Burrage, Jackiewicz, Nørsett and Renaut by incorporating all terms in the expansion of the error of waveform relaxation iterations in the Laplace transform domain. Lower bounds for the size of the window of rapid convergence are also obtained. The theory is illustrated for waveform relaxation methods applied to differential systems resulting...
Generalization of the Bauer-Fike Theorem.
High-order finite difference schemes and Toeplitz based preconditioners for elliptic problems.
Incremental unknowns method and compact schemes
Incremental unknowns on nonuniform meshes
Inexact Newton preconditioning techniques for large symmetric eigenvalue problems.
Influence of preconditioning and blocking on accuracy in solving Markovian models
The article considers the effectiveness of various methods used to solve systems of linear equations (which emerge while modeling computer networks and systems with Markov chains) and the practical influence of the methods applied on accuracy. The paper considers some hybrids of both direct and iterative methods. Two varieties of the Gauss elimination will be considered as an example of direct methods: the LU factorization method and the WZ factorization method. The Gauss-Seidel iterative method...
Interior penalty discontinuous approximations of elliptic problems.
Joint domain-decomposition -LU preconditioners for saddle point problems.
-norm of iterates and the spectral radius of matrices
LDU decompositions with and well conditioned.
Lower Bounds for the Condition Number of Vandermonde Matrices.
Modified block-approximate factorization strategies.
Multigrid method with preconditioning on coarse level
An algorithm for using the preconditioned conjugate gradient method to solve a coarse level problem is presented.
Multigrid preconditioning and Toeplitz matrices.
Multilevel preconditioners for Lagrange multipliers in domain imbedding.
Multilevel preconditioning.
Multilevel Schwarz methods.
Multiplicative Schwarz Methods for Discontinuous Galerkin Approximations of Elliptic Problems
In this paper we introduce and analyze some non-overlapping multiplicative Schwarz methods for discontinuous Galerkin (DG) approximations of elliptic problems. The construction of the Schwarz preconditioners is presented in a unified framework for a wide class of DG methods. For symmetric DG approximations we provide optimal convergence bounds for the corresponding error propagation operator, and we show that the resulting methods can be accelerated by using suitable Krylov space solvers. A discussion...