ON METHODS WITH ASYNCHRONOUSAPPROXIMATION OF THE INVERSE OPERATOR FORNONLINEAR LEAST SQUARES PROBLEMS

Анотація

This paper addresses the development and study of iterative methods for solving nonlinear least squares problems that avoid the direct computation of matrix inverses. Specifically, we investigate sequential, synchronous, and asynchronous strategies for approximating the inverse operator within the Gauss-Newton method, the secant method, and a method with third-order convergence. We present the theoretical foundations of these approaches,
including their convergence conditions, and provide details on how they can be implemented in parallel computing environments. Numerical experiments on a series of benchmark problems illustrate the comparative performance of each method variant. In particular, we show that methods using asynchronous approximation of the inverse operator often converge in fewer iterations and with reduced computational time compared to both their
synchronous and sequential counterparts, as well as classical methods reliant on explicit matrix inversion. 

Key words: parallel iterative methods; nonlinear least square problem; inverse operator approximation; asynchronous computing.