NUMERICAL METHODS FOR COMPUTING TWO KINDS OF THE BEST HANKEL TENSOR APPROXIMATIONS

摘要

Hankel tensors and their approximation problems are of particular interest in the multidimensional seismic trace interpolator problem. In this paper, we investigate the numerical methods for two kinds of the best Hankel tensor approximation problems. Based on the Vandermonde decomposition of Hankel tensors, the Hankel tensor approximation problem with missing data is transformed into an unconstrained optimization problem, and then the BFGS method is used to solve it. For the Hankel tensor approximation problems with the interval constraint and box constraint, Dykstra's algorithm and its acceleration versions are designed to solve them. Numerical examples illustrate that these methods are feasible and effective.