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ACM Transactions on Mathematical Software (TOMS), Volume 38 Issue 3, April 2012

Using Multicomplex Variables for Automatic Computation of High-Order Derivatives
Gregory Lantoine, Ryan P. Russell, Thierry Dargent
Article No.: 16
DOI: 10.1145/2168773.2168774

The computations of the high-order partial derivatives in a given problem are often cumbersome or not accurate. To combat such shortcomings, a new method for calculating exact high-order sensitivities using multicomplex numbers is presented....

Parallel and Cache-Efficient In-Place Matrix Storage Format Conversion
Fred Gustavson, Lars Karlsson, Bo Kågström
Article No.: 17
DOI: 10.1145/2168773.2168775

Techniques and algorithms for efficient in-place conversion to and from standard and blocked matrix storage formats are described. Such functionality is required by numerical libraries that use different data layouts internally. Parallel...

Interactive Initialization and Continuation of Homoclinic and Heteroclinic Orbits in MATLAB
Virginie De Witte, Willy Govaerts, Yuri A. Kuznetsov, Mark Friedman
Article No.: 18
DOI: 10.1145/2168773.2168776

matcont is a matlab continuation package for the interactive numerical study of a range of parameterized nonlinear dynamical systems, in particular ODEs, that allows to compute curves of equilibria, limit points, Hopf points,...

Estimating Derivatives of Noisy Simulations
Jorge J. Moré, Stefan M. Wild
Article No.: 19
DOI: 10.1145/2168773.2168777

We employ recent work on computational noise to obtain near-optimal difference estimates of the derivative of a noisy function. Our analysis relies on a stochastic model of the noise without assuming a specific form of distribution. We use this...

Algorithm 917: Complex Double-Precision Evaluation of the Wright ω Function
Piers W. Lawrence, Robert M. Corless, David J. Jeffrey
Article No.: 20
DOI: 10.1145/2168773.2168779

This article describes an efficient and robust algorithm and implementation for the evaluation of the Wright ω function in IEEE double precision arithmetic over the complex plane.

Algorithm 918: specdicho: A MATLAB Program for the Spectral Dichotomy of Regular Matrix Pencils
Miloud Sadkane, Ahmed Touhami
Article No.: 21
DOI: 10.1145/2168773.2168780

Given a regular matrix pencil λB -- A and a positively oriented contour γ in the complex plane, the spectral dichotomy methods applied to λB -- A and γ consist in...

Algorithm 919: A Krylov Subspace Algorithm for Evaluating the ϕ-Functions Appearing in Exponential Integrators
Jitse Niesen, Will M. Wright
Article No.: 22
DOI: 10.1145/2168773.2168781

We develop an algorithm for computing the solution of a large system of linear ordinary differential equations (ODEs) with polynomial inhomogeneity. This is equivalent to computing the action of a certain matrix function on the vector representing...