Automatic differentiation of characterizing sequences (Q1263225)

This brief paper compiles the basic recursive formulas for the evaluation of gradients and Hessians without reference to any particular programming language or software implementation. Despite the reference to characterizing sequences in the title, the technique of forward automatic differentiation can be applied to any function that is evaluated by computer program (as is almost invariably the case in practice). Unfortunately, the paper does not yet mention the alternative reverse mode of automatic differentiation, which has recently attracted some interest [see, e.g., the reviewer, On automatic differentiation, Mathematical programming, Proc. 13th Int. Symp., Tokyo/Jap. 1988, Math. Appl., Jap. Ser. 6, 83-107 (1989)].