Picture of person typing on laptop with programming code visible on the laptop screen

World class computing and information science research at Strathclyde...

The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of Open Access research papers by University of Strathclyde researchers, including by researchers from the Department of Computer & Information Sciences involved in mathematically structured programming, similarity and metric search, computer security, software systems, combinatronics and digital health.

The Department also includes the iSchool Research Group, which performs leading research into socio-technical phenomena and topics such as information retrieval and information seeking behaviour.

Explore

A multigrid preconditioner for an adaptive Black-Scholes solver

Ramage, Alison and von Sydow, L. (2011) A multigrid preconditioner for an adaptive Black-Scholes solver. BIT Numerical Mathematics, 51 (1). pp. 217-233. ISSN 0006-3835

Full text not available in this repository. Request a copy from the Strathclyde author

Abstract

This paper is concerned with the efficient solution of the linear systems of equations that arise from an adaptive space-implicit time discretisation of the Black-Scholes equation. These nonsymmetric systems are very large and sparse, so an iterative method will usually be the method of choice. However, such a method may require a large number of iterations to converge, particularly when the timestep used is large (which is often the case towards the end of a simulation which uses adaptive timestepping). An appropriate preconditioner is therefore desirable. In this paper we show that a very simple multigrid algorithm with standard components works well as a preconditioner for these problems. We analyse the eigenvalue spectrum of the multigrid iteration matrix for uniform grid problems and illustrate the method’s efficiency in practice by considering the results of numerical experiments on both uniform grids and those which use adaptivity in space.