Abstract: Based on variant regularization operators, this paper sets up a class of spherical [l1]-regularization least squares approximation model. The algorithm is illustrated to solve this approximation problem by using well conditioned spherical t-design as sampling point sets. Finally, numerical experiments demonstrate the theoretical results can provide satisfactory approximation on the sphere, with or without the presence of data errors.

Key words: spherical polynomial approximation, spherical [t]-design, [l1]-regularization

摘要： 基于不同的正则化算子的选取，建立了一类球面上带[l1]-正则项最小二乘逼近模型。通过选取好条件的球面[t]-设计点作为采样点，展示了求解此逼近问题的算法。最后，通过数值例子展现了满意的逼近效果—精确数据和噪声污染的情形。

关键词: 球面多项式逼近, 球面t-设计, l1-正则化