โ Scribed by W.R. Paterson
No coin nor oath required. For personal study only.
Asymptotically, as the solution to an equation is approached, superlinearly convergent methods (SCM's) are faster than the method of successive substitution (MSS) and are less troubled by rounding error (Pizer. 1975). However, earlyin an iteration MSS may converge more quickly so that if modest accuracy is required MSS may be best. It is shown below that a sufl5cient condition for convergence of MSS is also a condition likely to imply superior performance of alternative methods, viz SCM's operating on a transformed variable. These methods also show superiority to SCM's operating on an untransformed variable.
๐ SIMILAR VOLUMES
We propose a melhod LO numerically evaluate Lhe lransformadon lo good action-angle variables in non-separable muludimensional systems This melhod\_ which ts based on the adiabatic hypothesis of classical mechamu. is very easy IO apply (formally and numexxally) and is show to yield excellent results.