Existence tests for solutions of nonlinear equations using Borsuk's theorem

SIAM Journal on Numerical Analysis

Volumn 43, Issue 3, 2005, Pages 1348-1361

  Frommer, Andreas ^a   Lang, Bruno ^a  

^a UNIVERSITY OF WUPPERTAL   (Germany)

Author keywords

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

Indexed keywords

COMPUTATIONAL COMPLEXITY; COMPUTATIONAL METHODS; DIGITAL ARITHMETIC; NUMERICAL ANALYSIS; THEOREM PROVING;

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

NONLINEAR EQUATIONS;

EID: 33745432313     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142903438148     Document Type: Article

References (15)

1. G. ALEFELD, A. FROMMER, G. HEINDL, AND J. MAYER, On the existence theorems of Kantorovich, Miranda and Borsuk, Electron. Trans. Numer. Anal., 17 (2004), pp. 102-111.
2. G. ALEFELD AND J. HERZBERGER, introduction to Interval Computation, Academic Press, New York, 1983.
3. G. ALEFELD, F. POTRA, AND Z. SHEN, On the existence theorems of Kantorovich, Moore and Miranda, Computing Suppl., 15 (2001), pp. 21-28.
4. M. BERZ, COSY INFINITY Version 8.1 Programming Manual, Tech. Rep. MSUHEP-20703, National Superconductor Cyclotron Laboratory, Michigan State University, East Lansing, MI, 2002.
5. M. BERZ AND G. HOFSTÄTTER, Computation and application of Taylor polynomials with interval remainder bounds, Reliable Comput., 4 (1998), pp. 83-97.
6. K. BORSUK, Drei Sätze über die n-dimensionale Sphäre, Fund. Math., 20 (1933), pp. 177-190.
7. K. DEIMLING, Nonlinear Functional Analysis, Springer, Berlin, Heidelberg, New York, 1985.
8. A. FROMMER, B. LANG, AND M. SCHNURR, A comparison of the Moore and Miranda existence tests, Computing, 72 (2004), pp. 349-354.
9. R. B. KEARFOTT, Rigorous Global Search: Continuous Problems, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996.
10. C. MIRANDA, Un' osservazione su un theorema di Brouwer, Bolletino Unione Mathematica Italiana, 3 (1940), pp. 5-7.
11. R. E. MOORE, A test for existence of solutions to nonlinear systems, SIAM J. Numer. Anal., 14 (1972), pp. 611-615.
12. R. E. MOORE AND J. B. KIOUSTELIDIS, A simple test for accuracy of approximate solutions to nonlinear (or linear) systems, SIAM J. Numer. Anal., 17 (1980), pp. 521-529.
13. L. B. RALL, A comparison of the existence theorems of Kantorovich and Moore, SIAM J. Nutner. Anal., 17 (1980), pp. 148-161.
14. M. SCHNURR, On the proofs some, statements concerning the theorems of Kantorovich, Moore and Miranda, Reliab. Comput., 11 (2005), pp. 77-85.
15. W. WALSTER, The Extended Real Interval System, http://www.mscs.mu.edu/ ~globsol/walster-papers.html, 1998.