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Verified numerical computation for nonlinear equations. (English) Zbl 1186.65056
This is a kind of a survey paper on verification methods for solving nonlinear equations. Fixed point iterations, Newton-like methods, and methods for nonsmooth equations are explained and discussed.

65G30Interval and finite arithmetic
65H05Single nonlinear equations (numerical methods)
65G20Algorithms with automatic result verification
Full Text: DOI Euclid
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[2] G. Alefeld, Inclusion methods for systems of nonlinear equations--the interval Newton method and modifications. Topics in Validated Computations, J. Herzberger (ed.), Elsevier, Amsterdam, 1994, 7--26. · Zbl 0822.65029
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[9] G. Alefeld, Z. Shen and Z. Wang, Enclosing solutions of linear complementarity problems for H-matrices. Reliable Computing,10 (2004), 423--435. · Zbl 1074.65066 · doi:10.1023/B:REOM.0000047093.79994.8f
[10] G. Alefeld and Z. Wang, Verification of solutions of almost linear complementarity problems. Annals of the European Academy of Sciences 2005, EAS Publishing House, 211--231.
[11] X. Chen, A verification method for solutions of nonsmooth equations. Computing,58 (1997), 281--294. · Zbl 0882.65038 · doi:10.1007/BF02684394
[12] R. Krawczyk, Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken. Computing,4 (1969), 187--201. · Zbl 0187.10001 · doi:10.1007/BF02234767
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