Fast Adaptive Cross-Sampling Scheme for the Sparsified Adaptive Cross Approximation

A fast adaptive cross-sampling (FACS) scheme for the sparsified adaptive cross approximation (SPACA) algorithm is proposed to improve the conventional uniform spatial sampling. The FACS adaptively samples each well-separated block pair in an iterative manner to reach a given sampling error. At each iteration, the FACS first selects a set of initial samples with uniform spatial distribution for each block, and then uses the adaptive cross approximation (ACA) to find the important samples from the initial samples. Compared to the uniform spatial sampling, the FACS is easier to control the sampling error and needs fewer samples for the same sampling error. By reducing the number of samples, the FACS can enhance the efficiency of the SPACA. Numerical results are shown to demonstrate the merits of the proposed scheme.