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  • Nonlinear equations  (3)
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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Computing 37 (1986), S. 59-70 
    ISSN: 1436-5057
    Keywords: 65H10 ; Nonlinear equations ; projection methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wir betrachten eine Block-Version des Nichtlinearen Projektions-Verfahrens mit einer optimalen Kontrolle. Dieses Verfahren wird zur Lösung von Gleichungssystemen verwendet, bei denen die Gleichungsanzahl kleiner oder gleich der Anzahl der Unbekannten ist. Ein lokaler Konvergenzsatz wird bewiesen. Ein numerischer Vergleich mit dem zyklischen Nichtlinearen Projektions-Verfahren wird angestellt.
    Notes: Abstract We consider a block version of the Nonlinear Projection Method under an optimal control. This method is applied to the solution of systems of equations where the number of equation is less than or equal to the number of unknowns. A local convergence theorem is proved. We present a numerical comparison with the cyclic Nonlinear Projection Method.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    BIT 20 (1980), S. 501-510 
    ISSN: 1572-9125
    Keywords: Nonlinear equations ; numerical solution ; Brent's method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We describe an implementation of a generalization of Brent's method for solving systems of nonlinear equations. Some important features of the algorithm, like step control, discretization of derivatives and stopping criteria, are discussed. In particular we give numerical experiences which show that a stopping criterion proposed by D. Gay is efficient.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    BIT 19 (1979), S. 236-243 
    ISSN: 1572-9125
    Keywords: Nonlinear equations ; sequential secant method ; order of convergence ; quasi-Newton methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We introduce three new implementations of the sequential secant method for solving nonlinear simultaneous equations. Following the ideas of Gragg and Stewart, we store orthogonal factorizations of some of the matrices involved. Degeneracy in the increments of the independent variable is corrected according to simple and theoretically justified procedures. Some numerical experiences are also given.
    Type of Medium: Electronic Resource
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