Introduction to Automatic Differentiation and MATLAB Object-Oriented Programming

An introduction to both automatic differentiation and object-oriented programming can enrich a numerical analysis course that typically incorporates numerical differentiation and basic MATLAB computation. Automatic differentiation consists of exact algorithms on floating-point arguments. This implem...

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Vydáno v:SIAM review Ročník 52; číslo 3; s. 545 - 563
Hlavní autor: Neidinger, Richard D.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Philadelphia Society for Industrial and Applied Mathematics 01.01.2010
Témata:
Algorithms
Coefficients
Computational mathematics
EDUCATION
Jacobians
Mathematical differentiation
Mathematical vectors
Numerical analysis
Object oriented programming
Partial derivatives
Scalars
Series convergence
Studies
Taylor series
ISSN:0036-1445, 1095-7200
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Shrnutí:An introduction to both automatic differentiation and object-oriented programming can enrich a numerical analysis course that typically incorporates numerical differentiation and basic MATLAB computation. Automatic differentiation consists of exact algorithms on floating-point arguments. This implementation overloads standard elementary operators and functions in MATLAB with a derivative rule in addition to the function value; for example, sin u will also compute (cos u) * u′, where u and u′ are numerical values. These methods are mostly one-line programs that operate on a class of value-and-derivative objects, providing a simple example of object-oriented programming in MATLAB using the new (as of release 2008a) class definition structure. The resulting powerful tool computes derivative values and multivariable gradients, and is applied to Newton's method for root-finding in both single and multivariable settings. To compute higher-order derivatives of a single-variable function, another class of series objects keeps Taylor polynomial coefficients up to some order. Overloading multiplication on series objects is a combination (discrete convolution) of coefficients. This idea leads to algorithms for other operations and functions on series objects. A survey of more advanced topics in automatic differentiation includes an introduction to the reverse mode (our implementation is forward mode) and considerations in arbitrary-order multivariable series computation.
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ISSN:0036-1445
1095-7200
DOI:10.1137/080743627