A comparison of the Moore and Miranda existence tests

Computing (Vienna/New York)

Volumn 72, Issue 3-4, 2004, Pages 349-354

  Frommer, A ^a,b   Lang, B ^a,b   Schnurr, M ^a,c  

^a Bergische Universität Wuppertal ^*

^b UNIVERSITY OF WUPPERTAL   (Germany)

^c UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

Computational verification; Interval analysis; Miranda's existence theorem; Moore's theorem; Nonlinear systems

Indexed keywords

BOUNDARY CONDITIONS; COMPUTATIONAL METHODS; FUNCTIONS; MATHEMATICAL MODELS; MATRIX ALGEBRA; PROBLEM SOLVING; THEOREM PROVING;

COMPUTATIONAL VERIFICATION; INTERVAL ANALYSIS; MIRANDA'S EXISTENCE THEOREM; MOORE'S THEOREM;

NONLINEAR SYSTEMS;

EID: 3042828486     PISSN: 0010485X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00607-004-0064-4     Document Type: Article

References (8)

1. Alefeld, G., Herzberger, J.: Introduction to interval computation. Academic Press 1983.
2. Alefeld, G., Potra, F., Shen, Z.: On the existence theorems of Kantorovich, Moore and Miranda. In: Alefeld, G., Chen, X. (eds) Topics in numerical analysis with special emphasis on nonlinear problems. Computing [Suppl 15], 21-28. Wien: Springer-Verlag 2001.
3. Alefeld, G., Shen, Z.: Miranda's theorem and the verification of linear complementarity problems. Technical report, Institut für Wissenschaftliches Rechnen und Mathematische Modellbildung, University of Karlsruhe 2001.
4. Kearfott, R. B.: Rigorous global search: continuous problems. Dordrecht: Kluwer Academic Publishers 1996.
5. Miranda, C.: Un' osservazione su un teorema di Brouwer. Bol. Un. Mat. Ital., Ser. 2, 5-7 (1940).
6. Moore, R. E.: A test for existence of solutions to nonlinear systems. SIAM J. Numer. Anal. 14, 611-615 (1977).
7. Moore, R. E., Kioustelidis, J. B.: A simple test for accuracy of approximate solutions to nonlinear (or linear) systems. SIAM J. Numer. Anal. 17, 521-529 (1980).
8. Schnurr, M.: On the proofs of some statements concerning the theorems of Kantorovich, Moore and Miranda. Technical report, Institut für Angewandte Mathematik, Universität Karlsruhe, 2003. Submitted for publication.