連分式的收斂性、誤差分析及其應(yīng)用.pdf

1、中國科學(xué)技術(shù)大學(xué)博士學(xué)位論文連分式的收斂性、誤差分析及其應(yīng)用姓名：趙歡喜申請學(xué)位級別：博士專業(yè)：計(jì)算數(shù)學(xué)指導(dǎo)教師：朱功勤2003.4.1AbstractTheapplicationsofcontinuedfractions3reoReⅡtiedtotheirpossibleconvergence，therefore，theconvergencecriteriaofcontinuedfractionsareimportantintheth

2、eoryofcontinuedfractionsIntheotherhand，notonlytheexistenceofalimit，butalsohowfastthislimitisapproachedbytheapproximants，hence，itisalsoimportanttohaveestimatesforthisspeedofconvergenceThisthesisconcernsconvergencetheorems

3、andtruncationerrorboundsforallkindsofcontinuedfractionswithapplicationstomatrixfunctioncomputationInchapter2，abackwardthreetermrecurrencealgorithmispresentedtoevaluatescalarcontinuedfractions，anditsrelationwithtraditiona

4、lforwardthreetermrecurrencealgorithmisdiscussedAsallapplicationofthisalgorithm，someformulaeforthedifferencebetweenapproximantsofscalarcontinuedfractionsaxegiverAfewconvergencetheoremsCintheclassicalsense)arepresentedOurc

5、onvergenceproofsare‘‘constructive”innatureandthusyieldtruncationerrorestimatesAlsoincludedinthischapterareresultsonspeedofconvergence，apracticalmethodforconstructingtheerrorboundandapplicationstoanumberofspecialscalarcon

6、tin—uedfractions，Thegivennumericalexamplesindicatetheerrorboundspresentedinthischarpterareindeedsharp1nchapter3。vector／matrixvMnsdcontinuedfractionsbasedonSamelsoninverseareconsideredInscalarcase，themainmethodswensetoder

7、ivetheconvergencecriteriaforcontinuedfractionsarebaseduponthreetermrecurrencerelationorsomeverynicemappingpropertiesoflinearfractionaltransformationsorvalueregionstechniquesforcontinuedfractionsHowever，inmoregeneralcase，

8、suchasinvector／martixvaluedcase，itshouldbenotedthatitappeardiffculttofindrecurrencerelationssimilartothefamousthreetermrecurrencerelationwhichconbeusedtoderivesurprisinglygoodresultsintheconvergencetheoryforscalarcontinu

9、edfractionsTherefore。thosemethedscannotbeusedintheproof8oftheconvergencecriteriaforvector／matrixvaluedcontinuedfractionsInthischapter，thebackwardthreetermrecurrencerelationpresentedinChapter2isgeneralisedtothevector／matr