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**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

**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 *λ***B** -- **A** and a positively oriented contour *γ* in the complex plane, the spectral dichotomy methods applied to *λ***B** -- **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...