B-spline quasi-interpolation on sparse grids
نویسندگان
چکیده
منابع مشابه
Sampling and Cubature on Sparse Grids Based on a B-spline Quasi-Interpolation
Let Xn = {x j }j=1 be a set of n points in the d-cube Id := [0, 1]d , and n = {φ j }j=1 a family of n functions on Id . We consider the approximate recovery of functions f on Id from the sampled values f (x1), . . . , f (xn), by the linear sampling algorithm Ln(Xn, n, f ) := ∑nj=1 f (x j )φ j . The error of sampling recovery is measured in the norm of the space Lq(I)-norm or the energy quasi-no...
متن کاملB-Spline Interpolation on Lattices
4 Generalized and Optimized Spline Calculation 8 4.1 Multidimensional Array Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4.2 Condensing Matrix Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4.3 Eliminating Nested Loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 4.4 Reduction of Product Tens...
متن کاملHigh dimensional polynomial interpolation on sparse grids
We study polynomial interpolation on a d-dimensional cube, where d is large. We suggest to use the least solution at sparse grids with the extrema of the Chebyshev polynomials. The polynomial exactness of this method is almost optimal. Our error bounds show that the method is universal, i.e., almost optimal for many different function spaces. We report on numerical experiments for d = 10 using ...
متن کاملINTERPOLATION BY HYPERBOLIC B-SPLINE FUNCTIONS
In this paper we present a new kind of B-splines, called hyperbolic B-splines generated over the space spanned by hyperbolic functions and we use it to interpolate an arbitrary function on a set of points. Numerical tests for illustrating hyperbolic B-spline are presented.
متن کاملInverse B-spline interpolation
B-splines provide an accurate and efficient method for interpolating regularly spaced data. In this paper, I study the applicability of B-spline interpolation in the context of the inverse interpolation method for regularizing irregular data. Numerical tests show that, in comparison with lower-order linear interpolation, B-splines lead to a faster iterative conversion in under-determined proble...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Complexity
سال: 2011
ISSN: 0885-064X
DOI: 10.1016/j.jco.2011.03.003