ASYMPTOTICALLY SHARP ERROR BOUNDS FOR A QUADRATURE RULE FOR CAUCHY PRINCIPAL VALUE INTEGRALS BASED ON PIECEWISE LINEAR INTERPOLATION

在线阅读 下载PDF 导出详情
摘要 ForthenumericalevaluationofCauchyprincipalvalueintegralsoftheformf(x)(x-λ)-1dxwithλ∈(-1,1)andf∈C1[-1,1],weinvestigatethequadratureformulaQ(n+1)Spl1[·;λ]obtainedbyreplacingtheintegrandfunctionfbyitspiecewiselinearinterpolantatanequidistantsetofnodesasproposedbyRabinoivitz(Math.Comp.,51:741-747,1988).WegiveupperboundsforthePeano-typeerrorconstantsfors∈{1,2}.ThesearethebestpossibleconstantsininequalitiesofthetypeFurthermore,weprovethatourupperboundsareasymptoticallysharp.
机构地区 不详
关键词 西南
出版日期 1995年04月14日(中国期刊网平台首次上网日期,不代表论文的发表时间)