A homotopy method for multikernel-based approximation

Time: 2022-06-15 16:13:00

In this paper, we propose several numerical tricks and show some related propositions and theorems to deal with the considerable computation resources required to solve the multilinear system associated with the multikernel-based approximation method. Moreover, a homotopy method is proved to be suitable for the multikernel-based approximation method, including the global convergence and the locally superlinear convergence. We also discuss some problems behind the choice of the truncated length M and the low-rank approximation. Finally, we perform several numerical experiments to evaluate the benefits of the multikernel-based approximation method and the higher speed of the proposed numerical tricks.

References:

1. Ying Lin, Yimin Wei and Qi Ye. A Homotopy method for multikernel-based approximation. Journal of Nonlinear Variational Analysis, 2022, 6(2): 139-154.

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