A MONOTONIC STARTER FOR SOLVING THE HYPERBOLIC KEPLER EQUATION BY NEWTON'S METHOD

被引：0

作者：

Elipe, A. ^{[1
,2
]}

Montijano, J. I. ^{[3
]}

Randez, L. ^{[3
]}

Calvo, M. ^{[3
]}

机构：

[1] Univ Zaragoza, Grp Mecan Espacial IUMA, E-50009 Zaragoza, Spain

[2] Univ Zaragoza, Ctr Univ Defensa, E-50009 Zaragoza, Spain

[3] Univ Zaragoza, Appl Math IUMA, E-50009 Zaragoza, Spain

来源：

ASTRODYNAMICS 2018, PTS I-IV | 2019年 / 167卷

关键词：

CONVERGENCE; BOUNDS;

D O I：

暂无

中图分类号：

V [航空、航天];

学科分类号：

08 ; 0825 ;

摘要：

This communication deals with the iterative solution of the sine hyperbolic Kepler's equation (SHK): F-g(S) = S - g arcsinh(S) - L = 0. Since this function is monotonic increasing and convex, any starter value S-0 such that F-g(S-0) > 0, leads to a Newton's sequence S-j monotic decreasing to the exact solution of SKE equation and therefore has some advantages over non monotonic starters. Because of this, we are able to construct a monotonic starter such that minimizes the computational cost and that guarantees super-convergence (q-convergence) by analyzing the error estimates of Newton's iteration. In contrast with other starters in which the quality is assessed by extensive numerical experiments, here we use theoretical tools to reach super-convergence.

引用

页码：57 / 71

页数：15