On a weighted quasi-residual minimization strategy for solving complex symmetric shifted linear systems.
On adaptive BDDC for the flow in heterogeneous porous media
We study a method based on Balancing Domain Decomposition by Constraints (BDDC) for numerical solution of a single-phase flow in heterogeneous porous media. The method solves for both flux and pressure variables. The fluxes are resolved in three steps: the coarse solve is followed by subdomain solves and last we look for a divergence-free flux correction and pressures using conjugate gradients with the BDDC preconditioner. Our main contribution is an application of the adaptive algorithm for selection...
On additive scharz preconditioners for sparse grid discretizations.
On algebraic multilevel methods for non-symmetric systems - convergence results.
On an accelerated procedure of extrapolation.
On an algorithm for testing T4 solvability of max-plus interval systems
In this paper, we shall deal with the solvability of interval systems of linear equations in max-plus algebra. Max-plus algebra is an algebraic structure in which classical addition and multiplication are replaced by and , where , . The notation represents an interval system of linear equations, where and are given interval matrix and interval vector, respectively. We can define several types of solvability of interval systems. In this paper, we define the T4 solvability and give an algorithm...
On Asymptotically Best Norms for Powers of Operators.
On block diagonal and Schur complement preconditioning.
On Condition Numbers and the Distance to the Nearest Ill-posed Problem.
On condition numbers of a nondefective multiple eigenvalue.
On Conjugate Gradient Type Methods and Polynomial Preconditioners for a Class of Complex Non-Hermitian Matrices.
On decomposition of k-tridiagonal ℓ-Toeplitz matrices and its applications
We consider a k-tridiagonal ℓ-Toeplitz matrix as one of generalizations of a tridiagonal Toeplitz matrix. In the present paper, we provide a decomposition of the matrix under a certain condition. By the decomposition, the matrix is easily analyzed since one only needs to analyze the small matrix obtained from the decomposition. Using the decomposition, eigenpairs and arbitrary integer powers of the matrix are easily shown as applications.
On Efficient Implementations of Kogbetliantz's Algorithm for Computing the Singular Value Decomposition.
On error estimation for the pseudosolution of an inconsistent linear system
On error estimation in the conjugate gradient method and why it works in finite precision computations.
On fast factorization pivoting methods for sparse symmetric indefinite systems.
On finite element approximation of fluid structure interaction by Taylor-Hood and Scott-Vogelius elements
This paper focuses on mathematical modeling and finite element simulation of fluid-structure interaction problems. A simplified problem of two-dimensional incompressible fluid flow interacting with a rigid structure, whose motion is described with one degree of freedom, is considered. The problem is mathematically described and numerically approximated using the finite element method. Two possibilities, namely Taylor-Hood and Scott-Vogelius elements are presented and implemented. Finally, numerical...
On Fixed Point Linear Equations.
On generalized methods of the transfer of conditions
The methods of the transfer of conditions are generalized so that they also cover the direct methods leading to the diagonalization of the original matrix of a system with a band matrix. Part 3 is devoted to the numerical stability of methods of the transfer of conditions described in author's previous paper. Finally, it is shown how to obtain a particular method by the choice parameters of the general algorithm.
On graded QR decompositions of products of matrices.