Volume 12, Issue 2
Discrete Least Squares Hybrid Approximation with Regularization on the Two-Sphere

Int. J. Numer. Anal. Mod., 12 (2015), pp. 328-342.

Published online: 2015-12

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• Abstract

In this paper we consider the discrete constrained least squares problem coming from numerical approximation by hybrid scheme on the sphere, which applies both radial basis functions and spherical polynomials. We propose a novel $l_2-l_1$ regularized least square model for this problem and show that it is a generalized model of the classical "saddle point" model. We apply the alternating direction algorithm to solve the $l_2-l_1$ model and propose a convenient stopping criterion for the algorithm. Numerical results show that our model is more efficient and accurate than other models.

• Keywords

Regularized least squares, hybrid approximation, alternating direction method.

65K05, 90C30

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@Article{IJNAM-12-328, author = {}, title = {Discrete Least Squares Hybrid Approximation with Regularization on the Two-Sphere}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2015}, volume = {12}, number = {2}, pages = {328--342}, abstract = {

In this paper we consider the discrete constrained least squares problem coming from numerical approximation by hybrid scheme on the sphere, which applies both radial basis functions and spherical polynomials. We propose a novel $l_2-l_1$ regularized least square model for this problem and show that it is a generalized model of the classical "saddle point" model. We apply the alternating direction algorithm to solve the $l_2-l_1$ model and propose a convenient stopping criterion for the algorithm. Numerical results show that our model is more efficient and accurate than other models.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/492.html} }
TY - JOUR T1 - Discrete Least Squares Hybrid Approximation with Regularization on the Two-Sphere JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 328 EP - 342 PY - 2015 DA - 2015/12 SN - 12 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/492.html KW - Regularized least squares, hybrid approximation, alternating direction method. AB -

In this paper we consider the discrete constrained least squares problem coming from numerical approximation by hybrid scheme on the sphere, which applies both radial basis functions and spherical polynomials. We propose a novel $l_2-l_1$ regularized least square model for this problem and show that it is a generalized model of the classical "saddle point" model. We apply the alternating direction algorithm to solve the $l_2-l_1$ model and propose a convenient stopping criterion for the algorithm. Numerical results show that our model is more efficient and accurate than other models.

Yang Zhou. (1970). Discrete Least Squares Hybrid Approximation with Regularization on the Two-Sphere. International Journal of Numerical Analysis and Modeling. 12 (2). 328-342. doi:
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