The shapeparameterintheGaussianfunctionII

摘要

This isacontinuationofourformerstudy,Luh 1, oftheshapeparameter β contained inGaussian e~(?βjxj2), x∈R~n. InsteadofusingtheerrorboundpresentedbyMadychandNelson 2, hereweadoptanimproved error boundconstructedbyLuhtoevaluatetheinfluence of β on errorestimates.Thisresultsinanewset of criteriafortheoptimalchoiceof β and muchsharpererrorestimatesforGaussianinterpolation.What is importantisthatthenotoriousill-conditioningofGaussianinterpolationcanbegreatlyrelieved because inthisapproachthe fill distanceneednotbeverysmall.