任意结点组上的截断Hermite插值收敛(英文)  

Convergence of Truncated Hermite Interpolation on an Arbitrary System of Nodes

作　　者：刘蓉[1] 史应光[1] 

机构地区：[1]湖南师范大学数学与计算机科学学院,高性能计算与随机信息处理省部共建教育部重点实验室(HPCSIP),中国长沙410081

出　　处：《湖南师范大学自然科学学报》2013年第4期1-6,共6页Journal of Natural Science of Hunan Normal University

基　　金：国家自然科学基金资助项目(11171100,11071064);湖南省研究生创新基金资助项目(CX2012B195,CX2012B198)

摘　　要：给出了任意结点组上截断Hermite插值的加权Lp范数收敛的充分条件.其中主要结论之一:给定一个整数r,0≤r≤m-1,函数f∈Cr[-1,1],记Hn,r(f;x)为任意结点组X上的Hermite插值多项式,设dμ为一个测度,0<p≤∞.设m k∈N o或者m k∈N e且m=max1≤k≤n m k≥3,r∈N0.进一步假设0≤r<q<m-1,r≤m-3.则sup‖f‖q'≤1‖Hn,q(f)‖dμ,p≤c(p,r)‖H n,r‖dμ,p,其中q'=min{q+1,m-1}.By applying the regular perturbation method and the secondorder averaging method, the sufficient conditions of the periodic solutions and the bifurcations in Duffing equation under the two resonant conditionsΩ∶〖KG-2mm〗ω∶〖KG-2mm〗ω0=2∶〖KG-2mm〗3∶〖KG-2mm〗1 and 1∶〖KG-2mm〗1/2∶〖KG-2mm〗1 are investigated. The numerical simulations not only show the consistence with the theoretical analysis, but also find some new complex behaviors, including the periodic2 bifurcation and the inverse periodic2 bifurcation to chaos, the chaos suddenly converge to period1,3 orbits, the jumping behaviors of period 1 orbit.

关 键 词：收敛 截断Hermite插值 任意结点组 

分 类 号：O241[理学—计算数学]