Optimal spline spaces of higher degree for L2 n-widths
نویسندگان
چکیده
In this paper we derive optimal subspaces for Kolmogorov n-widths in the L2 norm with respect to sets of functions defined by kernels. This enables us to prove the existence of optimal spline subspaces of arbitrarily high degree for certain classes of functions in Sobolev spaces of importance in finite element methods. We construct these spline spaces explicitly in special cases. Math Subject Classification: Primary: 41A15, 47G10, Secondary: 41A44
منابع مشابه
Optimal spline spaces of higher degree for L n-widths
In this paper we derive optimal subspaces for Kolmogorov n-widths in the L2 norm with respect to sets of functions defined by kernels. This enables us to prove the existence of optimal spline subspaces of arbitrarily high degree for certain classes of functions in Sobolev spaces of importance in finite element methods. We construct these spline spaces explicitly in special cases. Math Subject C...
متن کاملn - Widths of Sobolev Spaces in L p
Let W~ r) = {f:fecr-J[O, l ] , f (rl) abs. cont., Ilftr)IIp < oo}, and set B~) = {f: f~ ~ ' ) , I[/~r)llp ~ 1}. We find the exact Kolmogorov, Gerfand, linear, and Bernstein n-widths of B~p r) in L p for all pE(l, oo). For the Kolmogorov n-width we show that for n _> r there exists an optimal subspace of splines of degree r 1 with n r fixed simple knots depending on p,
متن کاملAn ${cal O}(h^{8})$ optimal B-spline collocation for solving higher order boundary value problems
As we know the approximation solution of seventh order two points boundary value problems based on B-spline of degree eight has only ${cal O}(h^{2})$ accuracy and this approximation is non-optimal. In this work, we obtain an optimal spline collocation method for solving the general nonlinear seventh order two points boundary value problems. The ${cal O}(h^{8})$ convergence analysis, mainly base...
متن کاملAbout Widths of Wiener Space in the Lq-Norm
In this paper we consider average n-widths of the Wiener space C in the Lq-norm. We study two kinds of average n-widths which describe best and best linear approximation of the Wiener space over all n-dimensional subspaces. The approximation problem on spaces with Wiener measure in the L2-norm was investigated in the book of Traub et al. (1988). Papers concerned with average n-widths in Banach ...
متن کاملMacro-elements and stable local bases for splines on Clough-Tocher triangulations
Macro-elements of arbitrary smoothness are constructed on Clough-Tocher triangle splits. These elements can be used for solving boundary-value problems or for interpolation of Hermite data, and are shown to be optimal with respect to spline degree. We believe they are also optimal with respect to the number of degrees of freedom. The construction provides local bases for certain superspline spa...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Journal of Approximation Theory
دوره 216 شماره
صفحات -
تاریخ انتشار 2017