Browsing by Subject "iterative methods"

Now showing 1 - 4 of 4

Access status: Open Access ,
A comparison of iterative methods of the cubic rate convergence in the problem of transformation between Cartesian and geodetic coordinates
(2014) Bajorek, Maciej; Kulczycki, Marek; Ligas, Marcin
The problem of transformation between Cartesian and geodetic (ellipsoidal) coordinates occurs often in day-to-day geodetic practice. Thus, from years it attracts interest of many scientists and practitioners. Despite the fact that many algorithms of the conversion exist to this day one may still observe new methods and approaches to the problem. In this work a comparison as to the efficiency of iterative methods of the cubic rate convergence to the solution of 'latitude equation' in three representations has been presented. Two of them are polynomial representations (quartic equations) and one is in the form of an irrational equation. A comparison has been performed on two ellipsoidal height intervals: from -10 km to 10 km, from 10 km to 36 000 km and from 0° to 90° for the latitude.
Access status: Open Access ,
Approximation methods for a class of discrete Wiener-Hopf equations
(2009) Nowak, Michał Andrzej
In this paper, we consider approximation methods for operator equations of the form $Au + Bu = f$, where $A$ is a discrete Wiener-Hopf operator on $l_{p}$ $1 \leq p \lt \infty$ which symbol has roots on the unit circle with arbitrary multiplicities (not necessary integers). Conditions on perturbation $B$ and $f$ are given in order to guarantee the applicability of projection-iterative methods. Effective error estimates, and simultaneously, decaying properties for solutions are obtained in terms of some smooth spaces.
Access status: Restricted ,
Obrazy numeryczne dla macierzy typu Toeplitza i ich zastosowania do teorii aproksymacji
(Data obrony: 2014-07-10) Syga, Aleksandra
Wydział Matematyki Stosowanej
Access status: Open Access ,
Some efficient seventh-order derivative-free families in root-finding
(2013) Soleymani, Fazlollah
The interest in efficient root-finding iterations is nowadays growing and influenced by the widespread use of high-speed computers. On the other hand, the calculation of derivatives is often hard, when the problems are formulated in terms of nonlinear equations and as a result, the importance of derivative-free methods emerges. For these reasons, some efficient three-step families of iterations for solving nonlinear equations are suggested, where the analytical proofs show their seventh-order error equations consuming only four function evaluations per iteration. We employ hard numerical test problems to illustrate the accuracy of the new methods from the families.