by Xiao Xu Han

A powerful computation model, Feed Forward Neural Networks (FFNNs) can be exployed to solve many problems in numerical computation which are difficult to solve by classical methods. A BP algorithm is briefly derived, and an improved version is given. An example of the technique is given: a problem of LU decomposion of an ill posed matrix which can not be solved by classical methods. Moreover, the Lusin theorem is extended to the two dimensional case. Using the theorem and universal approximation theorem of FFNNs, the author discusses the application of FFNNs in the numerical solution of ODE's and PDE's.