To the theory of the alternating triangle iteration method.
Toeplitz band matrices with exponentially growing condition numbers.
Total overlapping Schwarz' preconditioners for elliptic problems
A variant of the Total Overlapping Schwarz (TOS) method has been introduced in [Ben Belgacem et al., C. R. Acad. Sci., Sér. 1 Math. 336 (2003) 277–282] as an iterative algorithm to approximate the absorbing boundary condition, in unbounded domains. That same method turns to be an efficient tool to make numerical zooms in regions of a particular interest. The TOS method enjoys, then, the ability to compute small structures one wants to capture and the reliability to obtain the behavior of the solution...
Total overlapping Schwarz' preconditioners for elliptic problems
A variant of the Total Overlapping Schwarz (TOS) method has been introduced in [Ben Belgacem et al., C. R. Acad. Sci., Sér. 1 Math.336 (2003) 277–282] as an iterative algorithm to approximate the absorbing boundary condition, in unbounded domains. That same method turns to be an efficient tool to make numerical zooms in regions of a particular interest. The TOS method enjoys, then, the ability to compute small structures one wants to capture and the reliability to obtain the...
Towards robust 3D -pinch simulations: Discretization and fast solvers for magnetic diffusion in heterogeneous conductors.
Transfer functions and resolvent norm approximation of large matrices.
Transfer of boundary conditions for difference equations
It is well-known that the idea of transferring boundary conditions offers a universal and, in addition, elementary means how to investigate almost all methods for solving boundary value problems for ordinary differential equations. The aim of this paper is to show that the same approach works also for discrete problems, i.e., for difference equations. Moreover, it will be found out that some results of this kind may be obtained also for some particular two-dimensional problems.
Transforming a hierarchical into a unitary-weight representation.
Transient behavior of powers and exponentials of large Toeplitz matrices.
Triangular mesh analysis with application on hip bone
Shape analyses and similarity measuring is a very often solved problem in computer graphics. The shape distribution approach based on shape functions is frequently used for this determination. The experience from a comparison of ball-bar standard triangular meshes was used to match hip bones triangular meshes. The aim is to find relation between similarity measures obtained by shape distributions approach.
Truncated methods for large scale generalized eigenvalue problems.
Truncated spectral regularization for an ill-posed non-linear parabolic problem
It is known that the nonlinear nonhomogeneous backward Cauchy problem , with , where is a densely defined positive self-adjoint unbounded operator on a Hilbert space, is ill-posed in the sense that small perturbations in the final value can lead to large deviations in the solution. We show, under suitable conditions on and , that a solution of the above problem satisfies an integral equation involving the spectral representation of , which is also ill-posed. Spectral truncation is used...
Two Composition Methods for Solving Certain Systems of Linear Equations.
Two implementations of the preconditioned conjugate gradient method on heterogeneous computing grids
Efficient iterative solution of large linear systems on grid computers is a complex problem. The induced heterogeneity and volatile nature of the aggregated computational resources present numerous algorithmic challenges. This paper describes a case study regarding iterative solution of large sparse linear systems on grid computers within the software constraints of the grid middleware GridSolve and within the algorithmic constraints of preconditioned Conjugate Gradient (CG) type methods. We identify...
Two inverse eigenproblems for symmetric doubly arrow matrices.
Two preconditioners based on the multi-level splitting of finite element spaces.
Two simple derivations of universal bounds for the C.B.S. inequality constant
Universal bounds for the constant in the strengthened Cauchy-Bunyakowski-Schwarz inequality for piecewise linear-linear and piecewise quadratic-linear finite element spaces in 2 space dimensions are derived. The bounds hold for arbitrary shaped triangles, or equivalently, arbitrary matrix coefficients for both the scalar diffusion problems and the elasticity theory equations.
Two step extrapolation and optimum choice of relaxation factor of the extrapolated S.O.R. method
Limits of the extrapolation coefficients are rational functions of several poles with the largest moduli of the resolvent operator and therefore good estimates of these poles could be calculated from these coefficients. The calculation is very easy for the case of two coefficients and its practical effect in finite dimensional space is considerable. The results are used for acceleration of S.O.R. method.
Two-level additive Schwarz preconditioners for fourth-order mixed methods.
Two-sided approximations of inverses, square roots and Cholesky factors