Algorithms for projecting a point onto a level surface of a continuous function on a compact set (Q889159): Difference between revisions

The paper deals with the problem of finding a solution nearest to a given point for the equation \(f(x) = 0\), where \(f\) is an \(\varepsilon\)-Lipschitz continuous function. To solve the problem the authors propose two algorithms. The first algorithm is based on an idea similar to the second algorithm from \textit{V. I. Zabotin} and \textit{N. K. Arutyunova} [Zh. Vychisl. Mat. Mat. Fiz. 53, No. 3, 344--349 (2013; Zbl 1274.65065)]. It is an iterative algorithm in which the convergence to the set of zeros for the function is obtained by updating the value of \(\varepsilon\) depending on the current value of the function. The second algorithm is a generalization of the method from \textit{A. M. Dulliev} and \textit{V. I. Zabotin} [Zh. Vychisl. Mat. Mat. Fiz. 44, No. 5, 827--830 (2004); translation in Comput. Math. Math. Phys. 44, No. 5, 781--784 (2004; Zbl 1121.41034)]. After the introduction of the two algorithms the authors prove their convergence and show some numerical examples.