Hermite–Birkhoff interpolation on scattered data on the sphere and other manifolds
نویسندگان
چکیده
منابع مشابه
Scattered Data Fitting on the Sphere
We discuss several approaches to the problem of interpolating or approximating data given at scattered points lying on the surface of the sphere. These include methods based on spherical harmonics, tensor-product spaces on a rectangular map of the sphere, functions deened over spherical triangulations, spherical splines, spherical radial basis functions, and some associated multi-resolution met...
متن کاملScattered data approximation of fully fuzzy data by quasi-interpolation
Fuzzy quasi-interpolations help to reduce the complexity of solving a linear system of equations compared with fuzzy interpolations. Almost all fuzzy quasi-interpolations are focused on the form of $widetilde{f}^{*}:mathbb{R}rightarrow F(mathbb{R})$ or $widetilde{f}^{*}:F(mathbb{R})rightarrow mathbb{R}$. In this paper, we intend to offer a novel fuzzy radial basis function by the concept of so...
متن کاملNotes on Scattered-Data Radial-Function Interpolation
where α = (α1, . . . , αn) is an n-tuple of nonnegative integers and |α| = ∑n j=1 |αj |. If every polynomial p ∈ πm−1(R) is determined by its values on X, then we will say that the data set X is unisolvent (for πm−1(R )). This condition can also be rephrased in terms of matrices. Order the monomials x in some convenient way. Form the matrix P for which the rows are an x evaluated at xj , j = 1,...
متن کاملInterpolation and Scattered Data Fitting on Manifolds using Projected Powell-Sabin Splines
We present methods for either interpolating data or for fitting scattered data on a two-dimensional smooth manifold Ω. The methods are based on a local bivariate Powell-Sabin interpolation scheme, and make use of a family of charts {(Uξ , φξ)}ξ∈Ω satisfying certain conditions of smooth dependence on ξ. If Ω is a C2-manifold embedded into R3, then projections into tangent planes can be employed....
متن کاملPolynomial approximation on the sphere using scattered data
We consider the problem of approximately reconstructing a function f defined on the surface of the unit sphere in the Euclidean space R, using samples of f at scattered sites. A central role is played by the construction of a new operator for polynomial approximation, which is a uniformly bounded quasi–projection in the de la Vallée Poussin style, i.e. it reproduces spherical polynomials up to ...
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: Applied Mathematics and Computation
سال: 2018
ISSN: 0096-3003
DOI: 10.1016/j.amc.2017.05.018