Table of Contents
Computational Biology Journal
Volume 2013 (2013), Article ID 562767, 10 pages
http://dx.doi.org/10.1155/2013/562767
Research Article

Efficient Basis Change for Sparse-Grid Interpolating Polynomials with Application to T-Cell Sensitivity Analysis

Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA

Received 28 November 2012; Accepted 18 March 2013

Academic Editor: Željko Bajzer

Copyright © 2013 Gregery T. Buzzard. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Sparse-grid interpolation provides good approximations to smooth functions in high dimensions based on relatively few function evaluations, but in standard form it is expressed in Lagrange polynomials. Here, we give a block-diagonal factorization of the basis-change matrix to give an efficient conversion of a sparse-grid interpolant to a tensored orthogonal polynomial (or gPC) representation. We describe how to use this representation to give an efficient method for estimating Sobol' sensitivity coefficients and apply this method to analyze and efficiently approximate a complex model of T-cell signaling events.