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Global convergence property of modified Levenberg-Marquardt methods for nonsmooth equations

Shou-qiang Du, Yan Gao (2011)

Applications of Mathematics

In this paper, we discuss the globalization of some kind of modified Levenberg-Marquardt methods for nonsmooth equations and their applications to nonlinear complementarity problems. In these modified Levenberg-Marquardt methods, only an approximate solution of a linear system at each iteration is required. Under some mild assumptions, the global convergence is shown. Finally, numerical results show that the present methods are promising.

Homotopy method for minimum consumption orbit transfer problem

Joseph Gergaud, Thomas Haberkorn (2006)

ESAIM: Control, Optimisation and Calculus of Variations

The numerical resolution of the low thrust orbital transfer problem around the Earth with the maximization of the final mass or minimization of the consumption is investigated. This problem is difficult to solve by shooting method because the optimal control is discontinuous and a homotopic method is proposed to deal with these difficulties for which convergence properties are established. For a thrust of 0.1 Newton and a final time 50% greater than the minimum one, we obtain 1786 switching times....

How to increase convergence order of the Newton method to 2 × m ?

Sanjay Kumar Khattri (2014)

Applications of Mathematics

We present a simple and effective scheme for forming iterative methods of various convergence orders. In this scheme, methods of various convergence orders, such as four, six, eight and ten, are formed through a modest modification of the classical Newton method. Since the scheme considered is a simple modification of the Newton method, it can be easily implemented in existing software packages, which is also suggested by the presented pseudocodes. Finally some problems are solved, to very high...

Interval solutions of linear interval equations

Jiří Rohn (1990)

Aplikace matematiky

It is shown that if the concept of an interval solution to a system of linear interval equations given by Ratschek and Sauer is slightly modified, then only two nonlinear equations are to be solved to find a modified interval solution or to verify that no such solution exists.

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