Continuous Regularized Least Squares Polynomial Approximation on the Sphere
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-08-20
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
In this paper, we consider the problem of polynomial reconstruction of smooth functions on the sphere from their noisy values at discrete nodes on the two-sphere.
The method considered in this paper is a weighted least squares form with a continuous regularization.
Preliminary error bounds in terms of regularization parameter, noise scale, and smoothness are proposed under two assumptions: the mesh norm of the data point set and the perturbation bound of the weight.
Condition numbers of the linear systems derived by the problem are discussed.
We also show that spherical tϵ-designs, which can be seen as a generalization of spherical t-designs, are well applied to this model.
Numerical results show that the method has good performance in view of both the computation time and the approximation quality.
American Psychological Association (APA)
Zhou, Yang& Kong, Yanan. 2020. Continuous Regularized Least Squares Polynomial Approximation on the Sphere. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-9.
https://search.emarefa.net/detail/BIM-1202044
Modern Language Association (MLA)
Zhou, Yang& Kong, Yanan. Continuous Regularized Least Squares Polynomial Approximation on the Sphere. Mathematical Problems in Engineering No. 2020 (2020), pp.1-9.
https://search.emarefa.net/detail/BIM-1202044
American Medical Association (AMA)
Zhou, Yang& Kong, Yanan. Continuous Regularized Least Squares Polynomial Approximation on the Sphere. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-9.
https://search.emarefa.net/detail/BIM-1202044
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1202044