【摘要】 我们构造一个n次样条s_n^*（x）,它是一个在给定的m个不同结点上对已给实函数f∈L_?²进行联合插值,满足s_n^*j（x₀+0）=f^j（x₀+0）,s_n^*j（x_m-0）=f^j（x_m-0）,s_n^*j（x_i）=f^j（x_i）,j=1,2,…,m-1,j=0,1,…,v;在L₂范数下,在f的所有同样性质的插值样条当中,它又是f的最佳逼近,且得到f∈C[a,b],n→∞时,有∥s_n^*-f∥L₂→O。更多还原

【Abstract】 We constructed the n-degree spline sn* (x). Which interpolated a given real-valued function f∈Lω2 at pre-assigned m distinct nodes and satisfies sn*(j)(x0+0) = f(j)(x0+0), sn*(j)(xm-0)=f(j)(xm-0), sn*(j)(xi)=f(j)(xi), i=1,2,…,m-1,j= 0,1,…,v; and is the best approximation of f in the L2-sense over all splines of degree≤n with the same interpolatory character. It is shown that the L2-error ‖sn*-f‖ L2→0 as n→∞ if f∈C[a,b].更多还原