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  Browse All Reviews > Mathematics Of Computing (G) > Numerical Analysis (G.1) > Quadrature And Numerical Differentiation (G.1.4) > Automatic Differentiation (G.1.4...)  
  1-7 of 7 Reviews about "Automatic Differentiation (G.1.4...)": Date Reviewed
  Efficient differentiable programming in a functional array-processing language
Shaikhha A., Fitzgibbon A., Vytiniotis D., Peyton Jones S.  Proceedings of the ACM on Programming Languages 3(ICFP): 1-30, 2019. Type: Article

Differentiable programming, or automatic differentiation, is a powerful technique in many fields, including dynamic systems, machine learning, and computer vision, mainly for solving nonlinear problems. Forward (versus reverse) differentiation bas...

Jul 20 2021
  The art of differentiating computer programs: an introduction to algorithmic differentiation
Naumann U.,  SIAM, Philadelphia, PA, 2012. 358 pp. Type: Book (978-1-611972-06-1)

A large part of my job for the last eight years has been dealing with the first- and second-order derivatives of financial instruments. Hence, I find myself intimately aware of the numerical inaccuracies and computation time complexity of finite d...

Dec 5 2012
  Evaluating derivatives: principles and techniques of algorithmic differentiation
Griewank A., Walther A.,  Society for Industrial and Applied Mathematics, Philadelphia, PA, 2008. 460 pp. Type: Book (9780898716597)

Evaluating derivatives of functions is a problem frequently encountered in various areas of scientific computing. This is especially important if the task at hand comes from a nonlinear problem, regardless of whether the precise background is in o...

Dec 12 2008
  Accurate numerical derivatives in MATLAB
Shampine L.  ACM Transactions on Mathematical Software 33(4): 26-es, 2007. Type: Article

The use of finite difference methods for approximating derivatives has historic roots (recall the definition of the derivative from calculus). The need for derivatives is fundamental in calculations solving nonlinear problems, as the use of Newton...

Feb 25 2008
  Using AD to solve BVPs in MATLAB
Shampine L., Ketzscher R., Forth S.  ACM Transactions on Mathematical Software 31(1): 79-94, 2005. Type: Article

A method for the numerical solution of two-point boundary value problems for ordinary differential equations, using MATLAB, is discussed in this paper. A classical algorithm for this problem has been proposed by Kierzenka and Shampine [1]. This me...

Apr 20 2005
  Error formulas for divided difference expansions and numerical differentiation
Floater M.  Journal of Approximation Theory 122(1): 1-9, 2003. Type: Article

The main result of this paper is a new remainder formula for divided difference expansions of the form based on relatively elementary properties of the symmetric polynomials
Nov 6 2003
  Algorithm 799: revolve: an implementation of checkpointing for the reverse or adjoint mode of computational differentiation
Griewank A., Walther A.  ACM Transactions on Mathematical Software 26(1): 19-45, 2000. Type: Article

This is an excellent paper, describing a variant (“revolve”) of the basic form for reverse differentiation for computing the gradient of a scalar valued function, which enables computing this gradient of a function using no more than f...

Oct 1 2000
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