連分式的誤差分析及有理插值中的連分式方法.pdf

1、。j78n839分類號洳3冉～噎碩士學(xué)位論文論文題目連分式的誤差分析及有理插值中的連分式方法作者姓名指導(dǎo)教師學(xué)科(專業(yè))所在學(xué)院提交日期答辯日期彭悅韓丹夫教授黃正達(dá)教授計(jì)算數(shù)學(xué)理學(xué)院二零零六年五月二零零六年六月AbstractThetheoremofcontinuedfractionsisanoldbranchofmathematicsitisappliedmoreandmorewidelywiththedevelopmentofsci

2、enceandtechnologyespeciallyonrationalinterpolantsTheapplmationsofcontinuedfractionsareconcernednearlywithitsconvergenceTherearetwomainpartsinmythesis：gettingtruncationerrorboundsofspecialcontinuedfractionsandanalysingcon

3、tinuedfractionsalgorithmonrationalinterpolantsAtfirst，IanalysedtheconvergenceofSleszynski—PringsheimandWorpitzkyeontinuedfractionsusingthebackwardrecurrencealgorithmofcontinuedfractions，andobtainedgoodtruncationerrorboun

4、dsofthemWllile，abouttheapplicationsofcontinuedfractionsonrationalinterpolantsanalgorithmusingcontinuedfractions，whichwascalledinversedifferencecontinuedfractionsmethod，cangetrationalinterpolantsfunctionseasilyInthethesis

5、，Ianalysedtheexistenceofinversedifference妒(。o，z1，，Xn)，tojudgeiftherationalinterpolantsproblemscanbesolvedbythemethod；furthermore，Ianalysedtheappearanceofinaccessiblepoints(Xk，Yk)wheninversedifferenceexists，andobtainedthe