, Volume 21, Issue 2, pp 113–125 | Cite as

A unified derivation of quasi-Newton methods for solving non-sparse and sparse nonlinear equations

  • R. P. Tewarson


An augmented quasi-Newton equation is solved by using theW-V generalized inverse to give a unified derivation of the known quasi-Newton methods for solving systems of nonlinear algebraic equations. This approach makes it possible to get new formulas for sparse and non-sparse systems, and also to determine what norms of the update matrices are minimized when several useful quasi-Newton update formulas are derived.


Computational Mathematic Algebraic Equation Nonlinear Equation Nonlinear Algebraic Equation Unify Derivation 
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Eine einheitliche Ableitung von Quasi-Newtonschen Methoden zur Lösung von nicht dünnbesetzten und dünnbesetzten nichtlinearen Gleichungen


Eine erweiterte Quasi-Newtonsche Gleichung wird gelöst unter Verwendung derW-V verallgemeinerten Inverse und ergibt eine einheitliche Ableitung der bekannten Quasi-Newtonschen Methode für die Lösung von nichtlinearen algebraischen Gleichungssystemen. Dieser Zugang ermöglicht es uns, neue Formeln für dünnbesetzte und nicht dünnbesetzte Systeme zu erhalten und auch zu bestimmen, welche Normen der Update-Matrizen bei verschiedenen brauchbaren Quasi-Newtonschen Update-Formeln minimisiert werden.


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Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • R. P. Tewarson
    • 1
  1. 1.Department of Applied Mathematics and StatisticsState University of New YorkStony BrookUSA

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