2-periodic trigonometric interpolation problems on 2n equidistant nodes and 4n+1 equi- distant nodes are considered respectively.Regularity theorems,fundamental polynomials and convergence rate of the corresponding in...2-periodic trigonometric interpolation problems on 2n equidistant nodes and 4n+1 equi- distant nodes are considered respectively.Regularity theorems,fundamental polynomials and convergence rate of the corresponding interpolations are given here.展开更多
目的为了克服以2π为周期的三角插值问题所对应的插值空间Tn,ε(ε=0或1)对平移运算和求导运算不封闭,给出以π为周期的反周期函数的2-周期(0,p(D))三角插值。方法采用不同于Franz-Jurgen Delvos等人(Franz-Jurgen Delvos.BIT,1993,33(1...目的为了克服以2π为周期的三角插值问题所对应的插值空间Tn,ε(ε=0或1)对平移运算和求导运算不封闭,给出以π为周期的反周期函数的2-周期(0,p(D))三角插值。方法采用不同于Franz-Jurgen Delvos等人(Franz-Jurgen Delvos.BIT,1993,33(1),113-123;Franz-Jurgen Delvos,Ludger Knoche,BIT,1999,39(3):430-450.)的研究方法,通过不断求解给出结果。结果与结论给出了问题正则的充分必要条件及正则时基多项式的明显表达式,即r2v(x)=-(1/n)sum from j=1 to 2n( C2j-1cos(2j-1)(x-x2v)-D2j-1sin(2j-1)(x-x2v))/(Δ2j-1) ,q2v+1(x)=1/n sum from j=1 to n(1/Δ2j-1)[A2j-1cos(2j-1)(x-x2v+1)-iB2j-1sin(2j-1)(x-x2v+1)],其中v=0,1,…,n-1。展开更多
文摘2-periodic trigonometric interpolation problems on 2n equidistant nodes and 4n+1 equi- distant nodes are considered respectively.Regularity theorems,fundamental polynomials and convergence rate of the corresponding interpolations are given here.
文摘目的为了克服以2π为周期的三角插值问题所对应的插值空间Tn,ε(ε=0或1)对平移运算和求导运算不封闭,给出以π为周期的反周期函数的2-周期(0,p(D))三角插值。方法采用不同于Franz-Jurgen Delvos等人(Franz-Jurgen Delvos.BIT,1993,33(1),113-123;Franz-Jurgen Delvos,Ludger Knoche,BIT,1999,39(3):430-450.)的研究方法,通过不断求解给出结果。结果与结论给出了问题正则的充分必要条件及正则时基多项式的明显表达式,即r2v(x)=-(1/n)sum from j=1 to 2n( C2j-1cos(2j-1)(x-x2v)-D2j-1sin(2j-1)(x-x2v))/(Δ2j-1) ,q2v+1(x)=1/n sum from j=1 to n(1/Δ2j-1)[A2j-1cos(2j-1)(x-x2v+1)-iB2j-1sin(2j-1)(x-x2v+1)],其中v=0,1,…,n-1。
