FAST DENSE MATRIX METHOD FOR THE SOLUTION OF INTEGRAL EQUATIONS OF THE SECOND KIND-中国Betway体育网页登陆

摘要 Wepresentafastalgorithmbasedonpolynomialinterpolationtoapproximatematricesarisingfromthediscretizationofsecond-kindintegralequationswherethekernelfunctioniseithersmooth,non-oscillatoryandpossessingonlyafinitenumberofsingularitiesoraproductofsuchfunctionwithahighlyoscillatorycoefficientfunction.Contrasttowavelet-likeapproximations,ourapproximationmatrixisnotsparse.However,theapproximationcanbeconstrucedinO(n)operationsandrequiresO(n)storage,wherenisthenumberofquadraturepointsusedinthediscretization.Moreover,thematrix-vectormultiplicationcostisoforderO(nlogn).Thusourschemeiswellsuitableforconjugategradienttypemethods.Ournumericalresultsindicatethatthealgorithmisveryaccurateandstableforhighdegreepolynomialinterpolation.

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FAST DENSE MATRIX METHOD FOR THE SOLUTION OF INTEGRAL EQUATIONS OF THE SECOND KIND

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