IDR explained.
Image restoration through subimages and confidence images.
Implementing parallel elliptic solver on a Beowulf cluster.
Improved convergence bounds for smoothed aggregation method: linear dependence of the convergence rate on the number of levels
The smoothed aggregation method has became a widely used tool for solving the linear systems arising by the discretization of elliptic partial differential equations and their singular perturbations. The smoothed aggregation method is an algebraic multigrid technique where the prolongators are constructed in two steps. First, the tentative prolongator is constructed by the aggregation (or, the generalized aggregation) method. Then, the range of the tentative prolongator is smoothed by a sparse linear...
Improved convergence estimate for a multiply polynomially smoothed two-level method with an aggressive coarsening
A variational two-level method in the class of methods with an aggressive coarsening and a massive polynomial smoothing is proposed. The method is a modification of the method of Section 5 of Tezaur, Vaněk (2018). Compared to that method, a significantly sharper estimate is proved while requiring only slightly more computational work.
Incremental unknowns for solving partial differential equations.
Incremental unknowns method and compact schemes
Incremental unknowns on nonuniform meshes
Inequality-based approximation of matrix eigenvectors
A novel procedure is given here for constructing non-negative functions with zero-valued global minima coinciding with eigenvectors of a general real matrix A. Some of these functions are distinct because all their local minima are also global, offering a new way of determining eigenpairs by local optimization. Apart from describing the framework of the method, the error bounds given separately for the approximation of eigenvectors and eigenvalues provide a deeper insight into the fundamentally...
Infinite products and paracontracting matrices.
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.
Iterative methods for operator equations with adjoint factorization.
Iterative Methods for Overflow Queuing Models II.
Iterative methods for solving large systems of linear equations
Iterative methods for solving the dual formulation arising from image restoration.
Iterative methods for the numerical solution of the boundary value problem of elasticity [Abstract of thesis]
Iterative methods with analytical preconditioning technique to linear complementarity problems: application to obstacle problems
For solving linear complementarity problems LCP more attention has recently been paid on a class of iterative methods called the matrix-splitting. But up to now, no paper has discussed the effect of preconditioning technique for matrix-splitting methods in LCP. So, this paper is planning to fill in this gap and we use a class of preconditioners with generalized Accelerated Overrelaxation (GAOR) methods and analyze the convergence of these methods for LCP. Furthermore, Comparison between our methods...
Iterative Nachverbesserung mit Fehlereingrenzung der Cholesky-Faktoren von Stieltjes-Matrizen.
Iterative solution of rectangular systems of linear algebraic equations