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 fluid structure interaction problems of the heated cylinder approximated by the finite element method
This study addresses the problem of the flow around circular cylinders with mixed convection. The focus is on suppressing the vortex-induced vibration (VIV) of the cylinder through heating. The problem is mathematically described using the arbitrary Lagrangian-Eulerian (ALE) method and Boussinesq approximation for simulating fluid flow and heat transfer. The fluid flow is modeled via incompressible Navier-Stokes equations in the ALE formulation with source term, which represent the density variation...
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.
On inverses of Vandermonde and confluent Vandermonde matrices.
On iterative methods of higher order for systems of linear algebraic equations
The paper is concerned with certain -degree iterative methods for the solution of linear algebraic systems. The successive approximation is determined by means of approximations , , , . In this article to each iterative method of the first degree some -degree iterative method is found in order to accelerate the convergence of the intial method.
On matrices with all minors negative.
On Minimal Gerschgorin Sets for Families of Norms.
On multiresolution methods in numerical analysis.