Product formulas and numerical algorithms

Chorin, A. J., T. J. R. Hughes, J. E. Marsden and M. McCracken

Comm. Pure Appl. Math., 31, (1978), 205-256

Abstract:

Product formulas constitute one of several bridges between numerical and functional analysis. In numerical analysis, they represent algorithms intended to approximate some evolution equation and, in functional analysis, they are used to prove estimates, existence and representation theorems.

Our aim is to survey the setting for product formulas and to discuss some recent results. Needless to say, we do not attempt to accommodate all the complex variations which occur in practical algorithms, nor the sharpest possible theoretical results. Nevertheless, we hope that our middle ground approach and some of the examples will be of interest to both groups. Because of its survey nature, we have not hesitated to include some well-known examples which are important for understanding the ideas.