Improved estimates for condition numbers of radial basis function interpolation matrices

Abstract We improve existing estimates for the condition number of matrices arising in radial basis function interpolation. To this end, we refine lower bounds on the smallest eigenvalue and upper bounds on the largest eigenvalue, where our upper bounds on the largest eigenvalue are independent of the matrix dimension (i.e., the number of interpolation points). We show that our theoretical results comply with recent numerical observations concerning the condition number of radial basis function interpolation matrices.

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