SIAM Journal on Scientific Computing
The complex-step derivative approximation
ACM Transactions on Mathematical Software (TOMS)
Solving ODEs with MATLAB
Using AD to solve BVPs in MATLAB
ACM Transactions on Mathematical Software (TOMS)
An efficient overloaded implementation of forward mode automatic differentiation in MATLAB
ACM Transactions on Mathematical Software (TOMS)
Source transformation for MATLAB automatic differentiation
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part IV
Computer algebra software for least squares and total least norm inversion of geophysical models
Computers & Geosciences
Using Multicomplex Variables for Automatic Computation of High-Order Derivatives
ACM Transactions on Mathematical Software (TOMS)
An efficient overloaded method for computing derivatives of mathematical functions in MATLAB
ACM Transactions on Mathematical Software (TOMS)
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Complex step differentiation (CSD) is a technique for computing very accurate numerical derivatives in languages that support complex arithmetic. We describe here the development of a CSD package in MATLAB called PMAD. We have extended work done in other languages for scalars to the arrays that are fundamental to MATLAB. This extension raises questions that we have been able to resolve in a satisfactory way. Our goal has been to make it as easy as possible to compute approximate Jacobians in MATLAB that are all but exact. Although PMAD has a fast option for the expert that implements CSD as in previous work, the default is an object-oriented implementation that asks very little of the user.