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Publications [#287414] of John A. Trangenstein

Papers Published

  1. More, JJ; Trangenstein, JA, On the global convergence of broydens method, Mathematics of Computation, vol. 30 no. 135 (January, 1976), pp. 523-540, American Mathematical Society (AMS) [doi]
    (last updated on 2021/10/21)

    We consider Broyden's 1965 method for solving nonlinear equations. If the mapping is linear, then a simple modification of this method guarantees global and Q- super linear convergence. For nonlinear mappings it is shown that the hybrid strategy for nonlinear equations due to Powell leads to R-super linear convergence provided the search directions form a uniformly linearly independent sequence. We then explore this last concept and its connection with Broyden's method. Finally, we point out how the above results extend to Powell's symmetric version of Broyden's method. © 1976, American Mathematical Society.

    convergence of numerical methods;nonlinear equations;
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