Regularization by Aggregation of Global and Local Data on the Sphere

Abstract

In the present paper we study how to combine a limited regional information with globally available noisy observations related to the quantity of interest through an ill-posed spherical pseudo-differential equation. We formulate such combination as a minimization problem involving two misfit terms and the penalty term in a reproducing kernel Hilbert space. Moreover, we illustrate the proposed scheme by a numerical example and discuss an aggregation of two approaches by a linear functional strategy for a better performance.

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CMAM considers original mathematical contributions to computational methods and numerical analysis with applications mainly related to PDEs. The journal is interdisciplinary while retaining the common thread of numerical analysis, readily readable and meant for a wide circle of researchers in applied mathematics.

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