Automatic computation of derivatives with the use of the multilevel differentiating technique. I: Algorithmic basis
Automatic computation of derivatives plays an important role for the effective solution of diverse computational problems in nonlinear programming, solution of systems of nonlinear equations, etc. For an overview, see \textit{L. B. Rall} [Automatic differentiation: techniques and applications (1981; Zbl 0473.68025)]. Among the approaches used are the so-called forward method (FM) and the backward method (BM), which are based, respectively, on variational and adjoint processes. Both approaches present the differentiated relationship in the form of a computational system whose structure is determined by the oriented computational graph and differ in that the FM computes the derivatives in the sequence answering the graph's orientation while the BM, in the backward sequence. The present paper suggests a differentiation method based upon a multilevel modular unification of FM and BM. With an increased flexibility for accurate differentiation, this method provides in many cases a reasonable compromise between time and memory. The structure of the method is in a good agreement with the conventional modular principle of programming which facilitates its software realization.
scientific article; zbMATH DE number 3958551
scientific article