Title

Error bounds for overdetermined and underdetermined generalized centred simplex gradients

Authors

Warren Hare, University of British Columbia Okanagan
Gabriel Jarry-Bolduc, University of British Columbia Okanagan
Chayne Planiden, University of Wollongong

Publication Name

IMA Journal of Numerical Analysis

Abstract

Using the Moore-Penrose pseudoinverse this work generalizes the gradient approximation technique called the centred simplex gradient to allow sample sets containing any number of points. This approximation technique is called the generalized centred simplex gradient. We develop error bounds and, under a full-rank condition, show that the error bounds have O(Δ2), where Δ is the radius of the sample set of points used. We establish calculus rules for generalized centred simplex gradients, introduce a calculus-based generalized centred simplex gradient and confirm that error bounds for this new approach are also O(Δ2). We provide several examples to illustrate the results and some benefits of these new methods.

Open Access Status

This publication may be available as open access

Volume

42

Issue

1

First Page

744

Last Page

770

Funding Number

2018-03865

Funding Sponsor

Natural Sciences and Engineering Research Council of Canada