School of Mathematics

Jitse Niesen — Software

Exponential integrators

• expmvp is the Matlab function described in "A Krylov Subspace Method for Option Pricing" by Jitse Niesen and Will Wright. It is an improved version of the phipm function. To install, copy the files expmvp.m and expmnorm.m to a directory where Matlab can find them.
• phipm is the Matlab package described in "A Krylov subspace algorithm for evaluating the φ-functions appearing in exponential integrators" by Jitse Niesen and Will Wright. To install, copy the files phipm.m and expmnorm.m to a directory where Matlab can find them. Alternatively, download phipm.tar.gz (8.4 MB) which contains these files and scripts to reproduce the plots in the paper.

Linear algebra

• I contributed the MatrixFunctions module to Eigen. Eigen is a C++ template library for linear algebra: vectors, matrices, and related algorithms. It aims to be versatile, fast, elegant and compiler-friendly. The MatrixFunctions module contains a general routine for the computations of analytic matrix functions, with specializations for the sine, cosine, hyperbolic sine, and hyperbolic cosine. The module also implements specific algorithms for the matrix exponential, logarithm and square root. All algorithms are taken from the literature.

Evans functions

• MagnusEvans.nb : Mathematica notebook file for evaluating the Evans function using Magnus integration. Written by Simon Malham, email simonm [at] ma.hw.ac.uk for details.
• evans_matlab.tar.gz : collection of Matlab scripts for evaluating the Evans function. This archive includes the Fisher problem, the autocatalysis problem (for various parameter values) and the Gray-Scott problem. Methods included are the fourth-order Magnus and Gauss-Legendre and the classical Runge-Kutta method. Type "help evans" to get an overview of the possibilities.
• scalar_fig.m : Matlab script for reproducing the plots in the paper "Evaluating the Evans function: Order reduction in numerical methods" by Simon Malham and Jitse Niesen.