Approximation of Kernel Matrices with Multilevel Circulant
Guohui Song
Department of Applied Mathematics
Illinois Institute of Technology
Kernel-based methods have gained popularity in a variety of fields such as approximation, interpolation, meshless methods, neural networks and machine learning. A common problem of these kernel-based methods is to calculate the inverses of the matrices generated by a kernel function and a set of points. However, the computational cost of calculating the inverses of kernel matrices is a major concern. This work focuses on developing fast algorithms for calculating the inverses by approximating the kernel matrices with related multilevel circulant matrices so that the fast Fourier transform can apply to reduce the computational cost of calculating the inverses to O(nlog(n)), where n is the size of the matrix.