REGULARIZATION METHOD FOR THE GENERALIZED MOMENT PROBLEM IN A FUNCTIONAL REPRODUCING KERNEL HILBERT SPACE

IF 0.9 4区 数学 Q2 MATHEMATICS Journal of Integral Equations and Applications Pub Date : 2023-03-01 DOI:10.1216/jie.2023.35.61
Qianru Liu, Lei Huang, Rui Wang
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Abstract

Functional reproducing kernel Hilbert spaces (FRKHSs) are appropriate function spaces in which we seek a target function from a finite number of non-point-evaluation functional data. We consider reconstructing a function from a finite number of generalized moment data via regularization in an FRKHS with respect to the generalized moment functionals. We construct specific FRKHSs and their associated FRKHS kernels with respect to two classes of generalized moment functionals, the Hamburger moment functionals and the trigonometric moment functionals. We solve the regularization problem in the resulting FRKHSs by the representer theorem. Numerical examples are presented to illustrate the better performance of regularization in an FRKHS than regularization in the square integrable functions space.
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泛函再现核Hilbert空间中广义矩问题的正则化方法
函数再现核希尔伯特空间(FRKHSs)是一种从有限数量的非点求值函数数据中寻求目标函数的合适函数空间。我们考虑在FRKHS中利用有限个数的广义矩数据对广义矩函数进行正则化重构。我们根据两类广义矩函数,汉堡包矩函数和三角矩函数,构造了特定的FRKHS及其相关的FRKHS核。我们用表征定理解决了得到的FRKHSs中的正则化问题。数值算例说明了在FRKHS中正则化比在平方可积函数空间中正则化具有更好的性能。
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来源期刊
Journal of Integral Equations and Applications
Journal of Integral Equations and Applications MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
1.30
自引率
0.00%
发文量
16
审稿时长
>12 weeks
期刊介绍: Journal of Integral Equations and Applications is an international journal devoted to research in the general area of integral equations and their applications. The Journal of Integral Equations and Applications, founded in 1988, endeavors to publish significant research papers and substantial expository/survey papers in theory, numerical analysis, and applications of various areas of integral equations, and to influence and shape developments in this field. The Editors aim at maintaining a balanced coverage between theory and applications, between existence theory and constructive approximation, and between topological/operator-theoretic methods and classical methods in all types of integral equations. The journal is expected to be an excellent source of current information in this area for mathematicians, numerical analysts, engineers, physicists, biologists and other users of integral equations in the applied mathematical sciences.
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