摘要
Weintroducemultilevelaugmentationmethodsforsolvingoperatorequationsbasedondirectsumdecompositionsoftherangespaceoftheoperatorandthesolutionspaceoftheoperatorequationandamatrixsplittingscheme.Weestablishageneralsettingfortheanalysisofthesemethods,showingthatthemethodsyieldapproximatesolutionsofthesameconvergenceorderasthebestapproximationfromthesubspace.Theseaugmentationmethodsallowustodevelopfast,accurateandstablenonconventionalnumericalalgorithmsforsolvingoperatorequations.Inparticular,forsecondkindequations,specialsplittingtechniquesareproposedtodevelopsuchalgorithms.Thesealgorithmsarethenappliedtosolvethelinearsystemsresultingfrommatrixcompressionschemesusingwavelet-likefunctionsforsolvingFredholmintegralequationsofthesecondkind.Forthisspecialcase,acompleteanalysisforcomputationalcomplexityandconvergenceorderispresented.Numericalexamplesareincludedtodemonstratetheefficiencyandaccuracyofthemethods.IntheseexamplesweusetheproposedaugmentationmethodtosolvelargescalelinearsystemsresultingfromtherecentlydevelopedwaveletGalerkinmethodsandfastcollocationmethodsappliedtointegralequationsofthesecondkind.Ournumericalresultsconfirmthatthisaugmentationmethodisparticularlyefficientforsolvinglargescalelinearsystemsinducedfromwaveletcompressionschemes.
出版日期
2005年01月11日(中国期刊网平台首次上网日期,不代表论文的发表时间)