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A globally convergent algorithm for computing fixed points of \(C^2\) maps. (English) Zbl 0445.65032


MSC:

65H10 Numerical computation of solutions to systems of equations
54H25 Fixed-point and coincidence theorems (topological aspects)
68Q25 Analysis of algorithms and problem complexity

Citations:

Zbl 0398.65029

Software:

RKF45
Full Text: DOI

References:

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[12] Li, T. Y., Private communication (Sept. 1976)
[13] T.Y. Li, A rigorous algorithm for fixed point computation, unpublished.; T.Y. Li, A rigorous algorithm for fixed point computation, unpublished.
[14] Merrill, O., Applications and extensions of an algorithm to compute fixed points of upper semicontinuous mappings, Doctoral thesis (1972), I.O.E. Dept., Univ. of Michigan: I.O.E. Dept., Univ. of Michigan Ann Arbor, Mich
[15] Ortega, J. M.; Rheinboldt, W. C., Iterative Solution of Nonlinear Equations in Several Variables (1970), Academic: Academic New York · Zbl 0241.65046
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[17] Scarf, H., The approximation of fixed points of a continuous mapping, SIAM J. Appl. Math., 15, 1328-1343 (1967) · Zbl 0153.49401
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[21] Watts, H. A.; Shampine, L. F., The art of writing a Runge-Kutta code: RKF45, SIAM National meeting (June 1975), Rensselaer Polytechnic Institute: Rensselaer Polytechnic Institute Troy, N.Y, paper presented at
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