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• W423242012 abstract "Title of thesis: IMPROVING RADIAL BASIS FUNCTION INTERPOLATION VIA RANDOM SVD PRECONDITIONERS AND FAST MULTIPOLE METHODS Kerry Cheng, Master of Science, 2013 Thesis directed by: Professor Ramani Duraiswami Department of Computer Science Recent research in fast-multipole algorithms has yielded approximation algorithms that compute specific matrix vector products to any specified accuracy in linear time. This thesis tries to combine this with recent research in randomized algorithms that has developed fast ways to compute rank-k SVDs of an M ×N matrix. This combination yields an approximate SVD in O(kmax(M,N)) time. We demonstrate this and explore its use in developing a novel scattered-data interpolation algorithm in three dimensions. The use of sinc functions in three dimensions is also explored, specifically their ability to accurately interpolate some standard functions. We find that the width parameter plays an important role, and suggest a prescription for its selection. As with other RBF interpolation algorithms, interpolating N points requires the solution of a dense linear system, which has O(N) cost. We explore two uses of the fast randomized SVD to reduce this cost. First, we use the randomized SVD to come up with a solution to the linear system. Next, we use a preconditioned Krylov iterative method (GMRES) with a low rank SVD as a preconditioner. Results are presented, and the method is found promising. IMPROVING RADIAL BASIS FUNCTION INTERPOLATION VIA RANDOM SVD PRECONDITIONERS AND FAST MULTIPOLE METHODS" @default.
• W423242012 created "2016-06-24" @default.
• W423242012 creator A5073473218 @default.
• W423242012 date "2013-01-01" @default.
• W423242012 modified "2023-09-26" @default.
• W423242012 title "Improving radial basis function interpolation via random SVD preconditioners and fast multipole methods" @default.
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• W423242012 doi "https://doi.org/10.13016/m2dw23" @default.
• W423242012 hasPublicationYear "2013" @default.
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