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