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  • 1
    Electronic Resource
    Electronic Resource
    Efficient methods for enclosing solutions of systems of nonlinear equations (1990)
    Springer
    Computing 44 (1990), S. 221-235 
    Details
    ISSN: 1436-5057
    Keywords: 65G10 ; 65H10 ; Newton's method ; Newton-Gauss-Seidel method ; nonlinear equations ; R-order ; interval analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wir betrachten Modifikationen des Intervall-Newton-Verfahrens, welche zwei Ansätze miteinander verbinden: Mehrfache (z.B.s-fache) Verwendung derselben Auswertung der Jacobi-Matrix und näherungsweise Lösung der Newton-Gleichung mit einem „linearen” Iterationsprozeß. Insbesondere zeigen wir, daß dieR-Ordnung dieser Verfahrens+1 werden kann. Wir illustrieren unsere Ergebnisse an einem numerischen Beispiel.
    Notes: Abstract We consider modifications of the interval Newton method which combine two ideas: Reusing the same evaluation of the Jacobian several (says) times and approximately solving the Newton equation by some ‘linear’ iterative process. We show in particular that theR-order of these methods may becomes+1. We illustrate our results by a numerical example.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02262218
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Numerical validation for an inverse matrix eigenvalue problem (1994)
    Springer
    Computing 53 (1994), S. 311-322 
    Details
    ISSN: 1436-5057
    Keywords: 65F15 ; 65G10 ; Inverse eigenvalue problem ; enclosure for the inverse eigenvalue problem ; interval computation ; Newton's method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wir geben einen Algorithmus an, mit dem man Lösungen eines additiven inversen Matrizen-Eigenwertproblems nachweisen kann. Der Algorithmus beruht auf dem Newton-Verfahren, für das ein neues Abbruchkriterium verwendet wird. Er liefert enge Schranken für die Lösungen des Problems und garantiert so die meisten ihrer führenden Ziffern in einem gegebenem Gleitpunktsystem.
    Notes: Abstract We describe an algorithm with which one can verify solutions of an additive inverse matrix eigenvalue problem. The algorithm is based on Newton's method using a new criterion for terminating the iteration. In addition, it yields tight interval bounds for the solutions of the problem, thus guaranteeing most of their leading digits in a given floating point system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02307382
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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