research-article

An efficient overloaded method for computing derivatives of mathematical functions in MATLAB

Authors:

Michael A. Patterson,

Matthew Weinstein,

Anil V. RaoAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 39, Issue 3

Article No.: 17, Pages 1 - 36

https://doi.org/10.1145/2450153.2450155

Published: 03 May 2013 Publication History

Abstract

An object-oriented method is presented that computes without truncation the error derivatives of functions defined by MATLAB computer codes. The method implements forward-mode automatic differentiation via operator overloading in a manner that produces a new MATLAB code that computes the derivatives of the outputs of the original function with respect to the differentiation variables. Because the derivative code has the same input as the original function code, the method can be used recursively to generate derivatives of any order desired. In addition, the approach developed in this article has the feature that the derivatives are generated by simply evaluating the function on an instance of the class, thus making the method straightforward to use while simultaneously enabling differentiation of highly complex functions. A detailed description of the method is presented and the approach is illustrated and shown to be efficient on four examples.

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Yang YHou ZChen HLu P(2023)DRL-based Path Planner and its Application in Real Quadrotor with LIDARJournal of Intelligent and Robotic Systems10.1007/s10846-023-01819-0107:3Online publication date: 13-Mar-2023
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Brady NMees MVereecken PSafari M(2021)Implementation of Dual Number Automatic Differentiation with John Newman’s BAND AlgorithmJournal of The Electrochemical Society10.1149/1945-7111/ac3274168:11(113501)Online publication date: 8-Nov-2021
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Index Terms

An efficient overloaded method for computing derivatives of mathematical functions in MATLAB
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Numerical differentiation
    2. Quadrature

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cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 39, Issue 3

April 2013

149 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/2450153

Issue’s Table of Contents

Copyright © 2013 ACM.

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Publication History

Published: 03 May 2013

Accepted: 01 September 2012

Revised: 01 August 2012

Received: 01 December 2011

Published in TOMS Volume 39, Issue 3

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Majidian H(2024)A comparative study of Filon-type rules for oscillatory integralsJournal of Numerical Analysis and Approximation Theory10.33993/jnaat531-138053:1(132-145)Online publication date: 6-Mar-2024
https://doi.org/10.33993/jnaat531-1380
Yang YHou ZChen HLu P(2023)DRL-based Path Planner and its Application in Real Quadrotor with LIDARJournal of Intelligent and Robotic Systems10.1007/s10846-023-01819-0107:3Online publication date: 13-Mar-2023
https://dl.acm.org/doi/10.1007/s10846-023-01819-0
Brady NMees MVereecken PSafari M(2021)Implementation of Dual Number Automatic Differentiation with John Newman’s BAND AlgorithmJournal of The Electrochemical Society10.1149/1945-7111/ac3274168:11(113501)Online publication date: 8-Nov-2021
https://doi.org/10.1149/1945-7111/ac3274
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