Further improvement of the Newton-PCG algorithm with automatic differentiation

Abstract

A new Newton-Preconditioned Conjugate Gradient (PCG) like algorithm is derived in [1,2], where the usual symbolic differentiation is used. Dixon in [3] pointed out that a further improvement would be achieved if symbolic differentiation is replaced by automatic differentiation. This paper confirms his observation showing how much further improvement can be obtained

Keywords:

• Newton's method
• Preconditioned conjugate gradient method
• Automatic differentiation