http://www.cs.kuleuven.ac.be/publicaties/rapporten/tw/TW528.pdf

Stable high-order quadrature rules with equidistant points

Suppose K is a convex polyhedral cone in En and is defined in terms of some generating set {ej, e2,   , eN} A procedure is devised so that, given any point q E En, the nearest point p in K to q can be found as a positive linear sum of N* 0, fE G4, i-1 for a positive linear functional L acting on a suitable finite-dimensional function space (D

/pdf/a-nearest-point-algorithm-for-convex-polyhedral-cones-and-46m2288abf.pdf

A nearest point algorithm for convex polyhedral cones and applications to positive linear approximation

Fast formation and assembly of finite element matrices with application to isogeometric linear elasticity

SUMMARY

Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled numerical models is to facilitate the communication of information across physics, scale, and domain interfaces, as well as between the iterations of solvers used for response computations. In a probabilistic context, any information that is to be communicated between subproblems or iterations should be characterized by an appropriate probabilistic representation. Although the number of sources of uncertainty can be expected to be large in most coupled problems, our contention is that exchanged probabilistic information often resides in a considerably lower-dimensional space than the sources themselves. In this work, we thus propose to use a dimension reduction technique for obtaining the representation of the exchanged information, and we propose a measure transformation technique that allows subproblem implementations to exploit this dimension reduction to achieve computational gains. The effectiveness of the proposed dimension reduction and measure transformation methodology is demonstrated through a multiphysics problem relevant to nuclear engineering. Copyright © 2012 John Wiley & Sons, Ltd.

Measure transformation and efficient quadrature in reduced-dimensional stochastic modeling of coupled problems

Stable high-order cubature formulas for experimental data

A general algorithm is presented for determining numerical integration formulas exact for an arbitrary finite set of continuous functions defined on a compact set, involving nonnegative combinations of function values at a finite number of points in the set. Examples are given. f

/pdf/a-general-algorithm-for-nonnegative-quadrature-formulas-1vmwvgg45j.pdf

A general algorithm for nonnegative quadrature formulas

The purpose of this paper is two-fold. Firstly, we explore some of the intimate connections between discrete least squares processes and quadratures. Secondly, we present an algorithm to construct Gauss-type integration formulas, and consider briefly the method proposed by Gautschi [2].

/pdf/discrete-least-squares-and-quadrature-formulas-50o73eqjwc.pdf

M. Wayne Wilson

Papers

A general algorithm for nonnegative quadrature formulas

Discrete least squares and quadrature formulas