Hermitian and skew-Hermitian splitting method on a progressive-iterative approximation for least squares fitting

To solve the problems of curves and surfaces approximation with normalized totally positive bases, a new progressive and iterative approximation for least square fitting method called HSS-LSPIA is proposed, which is based on the HSS iterative approach for solving linear equations of LSPIA. The HSS-LSPIA format includes two iterations with iterative di fference vectors, each of which is distinct from the other. The approximate optimal positive constant, as well as convergence analyses, are provided. Furthermore, the HSS-LSPIA method can be faster than the ELSPIA, LSPIA, and WHPIA methods in terms of convergence speed. Numerical results verify this phenomenon.

Automated summary

A new progressive and iterative approximation method called HSS-LSPIA is proposed in this paper to solve the problems of curves and surfaces approximation. The method includes two iterations with iterative difference vectors, providing an approximate optimal constant and convergence analysis. It is faster than other methods in terms of convergence speed.