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  • 1
    Electronic Resource
    Electronic Resource
    How to Solve Nonlinear Equations When a Third Order Method is Not Applicable (1999)
    Springer
    BIT 39 (1999), S. 255-269 
    Details
    ISSN: 1572-9125
    Keywords: Nonlinear equations ; Banach space ; second-order processes ; Newton's method ; Newton-Kantorovich assumptions ; majorizing sequences ; error bound
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we use a one-parametric family of second-order iterations to solve a nonlinear operator equation in a Banach space. A Kantorovich-type convergence theorem is proved, so that the first Fréchet derivative of the operator satisfies a Lipschitz condition. We also give an explicit error bound.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022389812813
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On a Convex Acceleration of Newton's Method (1999)
    Springer
    Journal of optimization theory and applications 100 (1999), S. 311-326 
    Details
    ISSN: 1573-2878
    Keywords: Nonlinear equations ; convex acceleration of Newton's method ; Newton–Kantorovich assumptions ; majorizing sequences
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this study, we use a convex acceleration of Newton's method (or super-Halley method) to approximate solutions of nonlinear equations. We provide sufficient convergence conditions for this method in three space settings: real line, complex plane, and Banach space. Several applications of our results are also provided.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1021730118905
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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