Coffee Time: 15:30 - 16:00. Kernel matrices can be found in computational physics, chemistry, statistics, and machine learning. Fast algorithms for matrix-vector multiplication for kernel matrices have been developed, and is a subject of continuing interest, including here at KAUST. One also often needs fast algorithms to solve systems of equations involving large kernel matrices. Fast direct methods can sometimes be used, for example, when the physical problem is 2-dimensional. In this talk, we address preconditioning for the iterative solution of kernel matrix systems. The spectrum of a kernel matrix significantly depends on the parameters of the kernel function used to define the kernel matrix, e.g., a length scale.

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