A discrete adapted hierarchical basis solver for radial basis function interpolation
نویسندگان
چکیده
منابع مشابه
A Discrete Adapted Hierarchical Basis Solver For Radial Basis Function Interpolation
In this paper we develop a discrete Hierarchical Basis (HB) to efficiently solve the Radial Basis Function (RBF) interpolation problem with variable polynomial order. The HB forms an orthogonal set and is adapted to the kernel seed function and the placement of the interpolation nodes. Moreover, this basis is orthogonal to a set of polynomials up to a given order defined on the interpolating no...
متن کاملA new stable basis for radial basis function interpolation
It is well-known that radial basis function interpolants suffer of bad conditioning if the basis of translates is used. In the recent work [12], the authors gave a quite general way to build stable and orthonormal bases for the native space NΦ(Ω) associated to a kernel Φ on a domain Ω ⊂ Rs. The method is simply based on the factorization of the corresponding kernel matrix. Starting from that se...
متن کاملA new trust-region algorithm based on radial basis function interpolation
Optimization using radial basis functions as an interpolation tool in trust-region (ORBIT), is a derivative-free framework based on fully linear models to solve unconstrained local optimization, especially when the function evaluations are computationally expensive. This algorithm stores the interpolation points and function values to using at subsequent iterations. Despite the comparatively ad...
متن کاملApproximation of a Fuzzy Function by Using Radial Basis Functions Interpolation
In the present paper, Radial Basis Function interpolations are applied to approximate a fuzzy function $tilde{f}:Rrightarrow mathcal{F}(R)$, on a discrete point set $X={x_1,x_2,ldots,x_n}$, by a fuzzy-valued function $tilde{S}$. RBFs are based on linear combinations of terms which include a single univariate function. Applying RBF to approximate a fuzzy function, a linear system wil...
متن کاملGrade Interpolation Using Radial Basis Function Networks
This paper analyses the application of Radial Basis Function (RBF) networks in grade interpolation. These networks are a very unique member of the family of Artificial Neural Networks. RBF networks have such theoretical properties that establish them as a potential alternative to existing grade interpolation techniques. Their suitability to the problem of grade interpolation will be demonstrate...
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: BIT Numerical Mathematics
سال: 2012
ISSN: 0006-3835,1572-9125
DOI: 10.1007/s10543-012-0397-x