Triangular decompositions for systems of polynomial equations with n variables, with exact coefficients are well-developed theoretically and in terms of implemented algorithms in computer algebra systems. However there is much less research about triangular decompositions for systems with approximate coefficients. In this paper we discuss the zero-dimensional case, of systems having finitely ma...

We consider applying the preconditioned conjugate gradient (PCG) method to solve linear systems Ax = b where the matrix A comes from the discretization of second-order elliptic operators. Let (L +)) ?1 (L t +) denote the block Cholesky factorization of A with lower block triangular matrix L and diagonal block matrix. We propose a preconditioner M = (^ L +)) ?1 (^ L t +) with block diagonal matr...

The study of frustrated spin systems often requires time-consuming numerical simulations. As the simplest approach, the classical Ising model is often used to investigate the thermodynamic behavior of such systems. Exploiting the small correlation lengths in frustrated Ising systems, we develop a method for obtaining first approximations to the energetic properties of frustrated two-dimensional...

We present a new approach for simplifying models composed of spline patches. Given an input model, the algorithm computes a new approximation of the model in terms of cubic triangular B ezier patches. It performs a series of geometric operations, consisting of patch merging and swapping diagonals, and makes use of patch connectivity information to generate C-LODs (curved levelsof-detail). Each ...

1.1 The number.dat data file from Shepard, Kilpatric, and Cunningham (1975). 11 3.1 A proximity matrix, morse digits.dat, for the 10 Morse code symbols representing the first ten digits 9.1 Order-constrained least-squares approximations to the digit proximity data of Shepard et al. (1975); the upper-triangular portion is anti-Robinson and the lower-triangular portion is strongly-anti-9.2 The 45...

in this paper a linear fuzzy fredholm integral equation(ffie) with arbitrary fuzzy function input and symmetric triangular (fuzzy interval) output is considered. for each variable, output is the nearest triangular fuzzy number (fuzzy interval) to the exact fuzzy solution of (ffie).

MOS surfaces are rational surfaces in R which provide rational envelopes of the associated two-parameter family of spheres. Moreover, all the offsets admit rational parameterizations as well. Recently, it has been proved that quadratic triangular Bézier patches in R are MOS surfaces. Following this result, we describe an algorithm for computing an exact rational envelope of a two-parameter fami...

In this paper we present a thorough set of numerical experiments to confirm the robustness of several Discontinuous Galerkin (DG) methods proposed for the approximation of Darcy law. We perform fairly twoand three-dimensional tests involving both low and high order approximations. Convergence tests carried out on Cartesian grids as well as on structured and unstructured triangular grids confirm...

in this paper, some elementary operations on triangular fuzzynumbers (tfns) are defined. we also define some operations on triangularfuzzy matrices (tfms) such as trace and triangular fuzzy determinant(tfd). using elementary operations, some important properties of tfms arepresented. the concept of adjoints on tfm is discussed and some of theirproperties are. some special types of tfms (e.g. pu...