Numerical analysis: Numerical analysis

TL;DR: This article examines some forms of function approximation, the solution of algebraic and functional equations, and numerical quadrature, and outlines some possibly less familiar topics, such as homotopy continuation and collocation methods.

Abstract: In this article, we touch on a few selected topics illustrating the interplay between computational statistics and numerical analysis. Rather than briefly reviewing a long array of methods, on one hand we place emphasis on problems, such as stochastic optimization, which require the joint application of several techniques; on the other hand, we stress a few recurring themes such as conditioning, numerical stability, convergence, and different discretization approaches that are at the root of many numerical methods. Then, we examine some forms of function approximation, the solution of algebraic and functional equations, and numerical quadrature. In particular, we outline some possibly less familiar topics, such as homotopy continuation and collocation methods. WIREs Comp Stat 2011 3 434–449 DOI: 10.1002/wics.172