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1998, VoI. 38, No. 4, pp. 619-635 0006-3835/98/3804-0619 $12.00
 

Summary: .- - - - - - --
BIT
1998, VoI. 38, No. 4, pp. 619-635
0006-3835/98/3804-0619 $12.00
@ Swets & Zeitlinger
MODIFICATIONS OF THE
INTERVAL-NEWTON-METHOD WITH IMPROVED
ASYMPTOTIC EFFICIENCY*.
G. E. ALEFELD\ F. A. POTRA2 and W. VÖLKERl
1Institute für Angewandte Mathematik, Universität Karlsruhe, D-76128 Karlsruhe
Germany. email: goetz.alefeld@mathematik.uni-karlsruhe.de
2Department of Mathematics, University of Iowa, Iowa City, IA 52242
USA. email: potra@math.uiowa.edu
Dedicated to U. Kulisch, Karlsruhe on the occasion of his 65th birthday
Abstract.
In this paper three new methods are introduced which compute lower and upper
bounds of a simple zero of areal function. The lower and upper bounds are converging
to this zero. Compared with the well-known Interval-Newton-Method, which has the
same properties and asymptotic efficiency 1.414. . . our optimal method has asymptotic
efficiency 1.839.. " The new methods have been extensively tested on a large set of

  

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

 

Collections: Mathematics