Optimal Approximations and Search for Feasible Circulant Matrix Embeddings for the Synthesis of Stationary Gaussian Random Fields

• Activity Number: 176
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Stefanos Kechagias*+ and Hannes Helgason and Vladas Pipiras
• Companies: University of North Carolina at Chapel Hill and University of Iceland and University of North Carolina at Chapel Hill
• Keywords: numerical synthesis ; Gaussian fields ; convex optimization ; circulant matrix embedding ; stationarity

Abstract

Circulant matrix embedding is one of the most popular and effective methods for efficient generation of Gaussian stationary univariate series. Although the idea of circulant matrix embedding has also been used for generation of Gaussian stationary random fields, there are many practical covariance structures of random fields where classical embedding methods break down. In this work we propose a novel methodology which adaptively constructs circulant embeddings. It is based on convex optimization with an objective function which measures the distance of the embedding covariance to the targeted covariance structure over the domain of interest. The optimal value of the objective function will be zero if and only if there exist an embedding for the a priori chosen embedding size. In cases where the optimum is nonzero, the resulting embedding covariance will be the optimal approximation to the targeted covariance.