A MATLAB Package For One Demensional Numerical Differentiation

The numerical differentiation is an important problem often encountered in the scientific research and engineering technologies. Because of its wide range of application backgrounds and solving difficulties caused by the ill-posed hess of very sensitive to the perturbation in the input data, many efforts have been given to the discussion and presentation of stable algorithms in solution settings. Comparatively, less attention has been paid to the development of applied software except for some Matlab codes of Murio and Hansen. So this thesis is devoted to develop a Matlab package for one dimensional numerical differentiation based on the existing effective algorithms that covers (1) regularized difference methods; (2) several kinds of Tikhonov's regularization methods and (3) mollification methods. The related algorithms (with corresponding references) are given and described, the six numerical differentiation routines with 8 test problems, are presented to compute the first or (and) second derivatives of the noisy data to be differentiated. The users can run the main program of deriv.m in a interactive way to test the functions of the package or write their own applied program by calling some related routines to do their business. A large number of simulation tests shown that the package contains rather complete functions, works stably and it is easy to use.