2008 JUN 2 - (VerticalNews.com) -- According to recent research from the United States, "The Dixon resultant method solves a system of polynomial equations by computing its resultant. It constructs a square matrix whose determinant (det) is a multiple of the resultant (res)."

  "The naive way to proceed is to compute det, factor it, and identify res. But often det is too large to compute or factor, even though res is relatively small. In this paper we describe three heuristic methods that often overcome these problems. The first, although sometimes useful by itself, is often a subprocedure of the second two. The second may be used on any polynomial system to discover factors of det without producing the complete determinant. The third applies when res appears as a factor of det in a certain exponential pattern. This occurs in some symmetrical systems of equations," wrote R.H. Lewis and colleagues, Fordham University ...read more

  2008 MAY 12 - (VerticalNews.com) -- "In this paper the problem of blending parametric surfaces is discussed. We present a constructing method of blending surfaces by parametric discrete interpolation PDE splines," investigators in Granada, Spain report.

  "These functions are obtained from some boundary conditions and a given interpolation data point set, by minimizing a functional associated with a partial differential equation (PDE) in a parametric finite element space. We formulate the corresponding problem and we establish a variational characterization of the solution and some convergence results," wrote A. Pasadas and colleagues, University of Granada ...read more

  2008 MAY 12 - (VerticalNews.com) -- "This paper presents an iterative alternating algorithm for solving an inverse problem in linear elasticity," investigators in France report.

  "A relaxation procedure is developed in order to increase the rate of convergence of the algorithm and two selection criteria for the variable relaxation factors are provided. The boundary element method is used in order to implement numerically the constructing algorithm," wrote A. Ellabib and colleagues ...read more