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A numerical algorithm for the solution of an inverse coefficient problem for nonstationary, nonlinear production-destruction type model is proposed and tested on an example of the Lorenz'63 system. With an ensemble of adjoint problem solutions, the inverse problem is transformed into a quasi-linear matrix problem and solved with Newton-type algorithm. Two different ways of the adjoint ensemble construction are compared. In the first one, a trigonometric basis is used. In the second one in situ measurements are taken into account. Local convergence properties of the algorithm are studied numerically to find out when the use of more data can lead to the degradation of the reconstruction results. [ABSTRACT FROM AUTHOR]

In this paper we study the convergence of Halley's method as a method for finding all zeros of a polynomial simultaneously. We present two types of local convergence theorems as well as a semilocal convergence theorem for Halley's method for simultaneous computation of polynomial zeros. [ABSTRACT FROM AUTHOR]