共查询到20条相似文献,搜索用时 15 毫秒
1.
Piecewise polynomial,positive definite and compactly supported radial functions of minimal degree 总被引:23,自引:0,他引:23
Holger Wendland 《Advances in Computational Mathematics》1995,4(1):389-396
We construct a new class of positive definite and compactly supported radial functions which consist of a univariate polynomial within their support. For given smoothness and space dimension it is proved that they are of minimal degree and unique up to a constant factor. Finally, we establish connections between already known functions of this kind. 相似文献
2.
Zuhua Luo 《Advances in Computational Mathematics》1999,10(3-4):261-270
In this paper, we obtain some sufficient conditions for positive definite kernels to be strictly positive definite and hence
well‐posed for Hermite scattered data interpolation on Euclidean unit spheres.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
3.
On interpolation with products of positive definite functions 总被引:1,自引:0,他引:1
Hans Strauss 《Numerical Algorithms》1997,15(2):153-165
In this paper we consider the problem of scattered data interpolation for multivariate functions. In order to solve this problem, linear combinations of products of positive definite kernel functions are used. The theory of reproducing kernels is applied. In particular, it follows from this theory that the interpolating functions are solutions of some varational problems. 相似文献
4.
Mohamed Allali Tomasz Przebinda 《Proceedings of the American Mathematical Society》2001,129(5):1459-1462
We recognize a result of Schreiner, concerning strictly positive definite functions on a sphere in an Euclidean space, as a generalization of Bochner's theorem for compact groups.
5.
《Expositiones Mathematicae》2022,40(3):395-408
We study the continuity and strict positive definiteness of positive definite functions on quasi-metric spaces given by integral transforms. We apply some of our findings to positive definite functions on the Euclidean space which are given by cosine transforms () and Fourier–Bessel transforms (). We also apply the results to positive definite functions on a general quasi-metric space realized as extensions of certain real Laplace transforms defined by conditionally negative definite functions on the quasi-metric space itself. 相似文献
6.
Gregory E. Fasshauer 《Advances in Computational Mathematics》1999,10(1):81-96
We show how conditionally negative definite functions on spheres coupled with strictly completely monotone functions (or functions whose derivative is strictly completely monotone) can be used for Hermite interpolation. The classes of functions thus obtained have the advantage over the strictly positive definite functions studied in [17] that closed form representations (as opposed to series expansions) are readily available. Furthermore, our functions include the historically significant spherical multiquadrics. Numerical results are also presented. This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
7.
Xingping Sun 《Numerical Algorithms》1994,7(2):253-268
In this paper, we study cardinal Hermite interpolation by using positive definite functions. Among other things, we establish a procedure that employs the multiquadrics for cardinal Hermite interpolation. 相似文献
8.
We give a sufficient condition for strictly positive definiteness in . The result is based on the question how sparse subsets of can be to guarantee linear independence of the exponentials. 相似文献
9.
Michael Schreiner 《Proceedings of the American Mathematical Society》1997,125(2):531-539
Recently, Xu and Cheney (1992) have proved that if all the Legendre coefficients of a zonal function defined on a sphere are positive then the function is strictly positive definite. It will be shown in this paper that, even if finitely many of the Legendre coefficients are zero, the strict positive definiteness can be assured. The results are based on approximation properties of singular integrals, and provide also a completely different proof of the results of Xu and Cheney.
10.
Herbert Heyer 《Periodica Mathematica Hungarica》2006,52(1):19-40
Summary The main aim of the paper is to prove still another version of the Lévy--Khintchine decomposition of conditionally positive
definite functions on a general locally compact Abelian group. The exposition is based on the two-cones theorem proved by
N. Drumm in 1976. Application of the main result to the Euclidean group shows the novelty of the approach. 相似文献
12.
We derive a set of differential inequalities for positive definite functions based on previous results derived for positive definite kernels by purely algebraic methods. Our main results show that the global behavior of a smooth positive definite function is, to a large extent, determined solely by the sequence of even-order derivatives at the origin: if a single one of these vanishes then the function is constant; if they are all non-zero and satisfy a natural growth condition, the function is real-analytic and consequently extends holomorphically to a maximal horizontal strip of the complex plane. 相似文献
13.
This contribution gives results on the action of the Laplace-Beltrami derivative on sufficiently smooth kernels on the sphere, those defined by absolutely and uniformly expansions generated by a family of at least continuous functions. Among other things, the results show that convenient Laplace-Beltrami derivatives of positive definite kernels on the sphere are positive definite too. We also include similar results on the action of the Laplace-Beltrami derivative on condensed spherical harmonic expansions. 相似文献
14.
本文给出了四次函数实零点的完全判据和正定条件,这一结果在研究多项式系统的奇点分析和分支问题时给出了可以实用的判据. 相似文献
15.
Summary This paper investigates some aspects of discrete least squares approximation by translates of certain classes of radial functions. Its specific aims are (i) to provide conditions under which the associated least squares matrix is invertible and (ii) to give upper bounds for the Euclidean norms of the inverses of these matrices (when they exist).The second named author was supported by the National Science Foundation under grant number DMS-8901345 相似文献
16.
We consider interpolation methods defined by positive definite functions on a locally compact group G. Estimates for the smallest and largest eigenvalue of the interpolation matrix in terms of the localization of the positive definite function on G are presented, and we provide a method to get positive definite functions explicitly on compact semisimple Lie groups. Finally, we apply our results to construct well-localized positive definite basis functions having nice stability properties on the rotation group SO(3). 相似文献
17.
18.
B. J. C. Baxter 《Constructive Approximation》1991,7(1):427-440
In [4], deep results were obtained concerning the invertibility of matrices arising from radial basis function interpolation. In particular, the Euclidean distance matrix was shown to be invertible for distinct data. In this paper, we investigate the invertibility of distance matrices generated byp-norms. In particular, we show that, for anyp(1, 2), and for distinct pointsx
1,,x
n
d
, wheren andd may be any positive integers, with the proviso thatn2, the matrixA
n×n
defined by
相似文献
19.
Let Ω⊂Rn be an open, connected subset of Rn, and let F:Ω−Ω→C, where Ω−Ω={x−y:x,y∈Ω}, be a continuous positive definite function. We give necessary and sufficient conditions for F to have an extension to a continuous positive definite function defined on the entire Euclidean space Rn. The conditions are formulated in terms of existence of a unitary representations of Rn whose generators extend a certain system of unbounded Hermitian operators defined on a Hilbert space associated to F. Different positive definite extensions correspond to different unitary representations. 相似文献
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