Abstract
In this paper we present a Quasi-Newton type method, which applies to large and sparse nonlinear systems of equations, and uses the Q-R factorization of the approximate Jacobians. This method belongs to a more general class of algorithms for which we prove a local convergence theorem. Some numerical experiments seem to confirm that the new algorithm is reliable.
Zusammenfassung
Wir stellen in dieser Arbeit ein Verfahren vom Quasi-Newton-Typ für große, dünnbesetzte nichtlineare Gleichungssysteme vor, das die QR-Faktorisierung der näherungsweisen Jacobi-Matrix benutzt. Das Verfahren gehört zu einer allgemeinen Klasse von Algorithmen, für die wir die lokale Konvergenz beweisen. Einige numerische Experimente deuten auf die Verläßlichkeit des neuen Algorithmus hin.
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Martínez, J.M. Quasi-Newton methods with factorization scaling for solving sparse nonlinear systems of equations. Computing 38, 133–141 (1987). https://doi.org/10.1007/BF02240178
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DOI: https://doi.org/10.1007/BF02240178