A Stable Richardson Iteration Method for Complex Linear Systems.
A Study of Semiiterative Methods for Nonsymmetric Systems of Linear Equations.
A subspace correction method for discontinuous Galerkin discretizations of linear elasticity equations
We study preconditioning techniques for discontinuous Galerkin discretizations of isotropic linear elasticity problems in primal (displacement) formulation. We propose subspace correction methods based on a splitting of the vector valued piecewise linear discontinuous finite element space, that are optimal with respect to the mesh size and the Lamé parameters. The pure displacement, the mixed and the traction free problems are discussed in detail. We present a convergence analysis of the proposed...
A twisted block tangential filtering decomposition preconditioner.
A two parameter iterative method for solving algebraic systems of domain decomposition type
An iterative procedure containing two parameters for linear algebraic systems originating from the domain decomposition technique is proposed. The optimization of the parameters is investigated. A numeric example is given as an illustration.
A unified approach to some strategies for the treatment of breakdown in Lanczos-type algorithms
The Lanczos method for solving systems of linear equations is implemented by using some recurrence relationships between polynomials of a family of formal orthogonal polynomials or between those of two adjacent families of formal orthogonal polynomials. A division by zero can occur in these relations, thus producing a breakdown in the algorithm which has to be stopped. In this paper, three strategies to avoid this drawback are discussed: the MRZ and its variants, the normalized and unnormalized...
A wavelet multigrid preconditioner for Dirichlet boundary value problems in general domains
A weak regular splitting for singular linear systems.
A well-conditioned integral equation for iterative solution of scattering problems with a variable Leontovitch boundary condition
The construction of a well-conditioned integral equation for iterative solution of scattering problems with a variable Leontovitch boundary condition is proposed. A suitable parametrix is obtained by using a new unknown and an approximation of the transparency condition. We prove the well-posedness of the equation for any wavenumber. Finally, some numerical comparisons with well-tried method prove the efficiency of the new formulation.
Abelovu cenu za rok 2019 získala Karen Uhlenbecková
Abelovu cenu získala v roce 2019 matematička Karen Uhlenbecková. Její práce mají důležitý dopad hned na několik oborů matematiky - geometrii, analýzu i matematickou fyziku. Zásadním způsobem ovlivnila moderní pojetí geometrické analýzy. V článku se pomocí relativně jednoduchých příkladů snažíme čtenáře seznámit se dvěma z oblastí, kterými se doposud zabývala. Na závěr též velmi stručně zmiňujeme hlavní výsledky několika jejích prací.
Absolute value equations with tensor product structure: Unique solvability and numerical solution
We consider the absolute value equations (AVEs) with a certain tensor product structure. Two aspects of this kind of AVEs are discussed in detail: the solvability and approximate solution. More precisely, first, some sufficient conditions are provided which guarantee the unique solvability of this kind of AVEs. Furthermore, a new iterative method is constructed for solving AVEs and its convergence properties are investigated. The validity of established theoretical results and performance of the...
Acceleration of convergence of a two-level algebraic algorithm by aggregation in smoothing process
A two-level algebraic algorithm is introduced and its convergence is proved. The restriction as well as prolongation operators are defined with the help of aggregation classes. Moreover, a particular smoothing operator is defined in an analogical way to accelarate the convergence of the algorithm. A model example is presented in conclusion.
Acceleration of convergence of a two-level algorithm by smoothing transfer operators
The technique for accelerating the convergence of the algebraic multigrid method is proposed.
Acceleration properties of the hybrid procedure for solving linear systems
The aim of this paper is to discuss the acceleration properties of the hybrid procedure for solving a system of linear equations. These properties are studied in a general case and in two particular cases which are illustrated by numerical examples.
Adaptive -step iterative methods for nonsymmetric systems of linear equations.
Adaptive mixed hybrid and macro-hybrid finite element methods.
Adaptive Procedure for Estimating Parameters for the Nonsymmetric Tchebychev Iteration.
Adaptive reduction-based multigrid for nearly singular and highly disordered physical systems.
Additional results on index splittings for Drazin inverse solutions of singular linear systems.
Additive Schwarz algorithms for parabolic convection-diffusion equations.