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I SClCntihc Computin~ R Strpkman CIaJ. I. ds )
 

Summary: I SClCntihc Computin~
R Strpkman CIaJ. I. ds )
~, IMACS!J'\orth.Hc,lJand Publisiunl Compan). 1983 ::;\
~HE CONVERGENCE OF SO~E INTERVAL-ARITHIU:TIC
~~DIFICATIONS OF NEWTON'S METHOD
Götz JI.lefcld
Insti tute of Applied Mathematics
" University of Karlsruhe
D-7500 KarlsruhejGerrnany
In this raper we consider the meamThile well-kno"Tninterval-arithmetic
mo~ifications of the.~ewton's method and of the so-called srmplified
Newton's ~ethod for solvir.gsystems of nonlinear equations. Starting
with an interval-v~ctor which contains a zero we give for the first time
sufficient conditions for the converoence of these'methods to th15 solu-
tion. If the starting interval-vecto~ contains no solution then under
the very sa~e conditions the methocs under consiceration will break down
after a finite n~~ber of steps. The interval-arithmetic eva1uatiop.of
thc first derivative is on1y involved in these conditions.
1. INTRODUCTION
-I:.

  

Source: Alefeld, Götz - Institut für Angewandte und Numerische Mathematik & Fakultät für Mathematik, Universität Karlsruhe

 

Collections: Mathematics