Abstract
In this paper we introduce a new Quasi-Newton method for solving nonlinear simultaneous equations. At each iteration only one column ofB k is changed to obtainB k+1 . This permits to use the well-known techniques of Linear Programming for modifying the factorization ofB k . We present a local convergence theorem for a restarted version of the method. The new algorithm is compared numerically with some other methods which were introduced for solving the same kind of problems.
Zusammenfassung
Wir stellen ein neues Quasi-Newton-Verfahren vor zur Lösung von nichtlinearen simultanen Gleichungen. Bei jeder Iteration wird lediglich eine Spalte vonB k verändert, umB k+1 zu erhalten. Dies erlaubt, wohlbekannte Techniken der Linearen Programmierung zur Faktorisierung vonB k zu benützen. Wir beweisen einen Satz über die lokale Konvergenz für die Methode. Der neue Algorithmus wird mit anderen bezüglich seiner numerischen Eigenschaften verglichen.
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Martínez, J.M. A Quasi-Newton method with modification of one column per iteration. Computing 33, 353–362 (1984). https://doi.org/10.1007/BF02242278
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DOI: https://doi.org/10.1007/BF02242278