Horner's rule for interval evaluation revisited

Computing (Vienna/New York)

Volumn 69, Issue 1, 2002, Pages 51-81

  Hartig, Jörg S ^a   Najafi Shoushtari, S Hani ^a   Grüne, Imke ^a   Yan, Amy ^b   Ellington, Andrew D ^b   Famulok, Michael ^a  

^a UNIVERSITY OF BONN   (Germany)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

Factorization; Interval arithmetic; Interval evaluation; Polynomial expression; Symbolic forms

Indexed keywords

COMPUTATIONAL METHODS; ERROR ANALYSIS; MATHEMATICAL MODELS; NUMERICAL METHODS; POLYNOMIALS; REAL TIME SYSTEMS;

INTERVAL ARITHMETIC; INTERVAL EVALUATIONS;

DIGITAL ARITHMETIC;

EID: 0036387347     PISSN: 0010485X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00607-002-1448-y     Document Type: Article

References (9)

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2. Bini, D., Mourrain, B.: Handbook of polynomial systems, 1996.
3. Ceberio, M., Granvilliers, L.: Solving nonlinear systems by constraint inversion and interval arithmetic. In: Proc. AISC'2000, 5th Int. Conf. on Artificial Intelligence and Symbolic Computation, vol. 1930 of LNAI, pp. 127-141, Madrid, Spain: Springer 2000.
4. Garloff, J., Graf, B.: Solving strict polynomial inequalities by bernstein expansion. In: The Use of Symbolic Methods in Control System Analysis and Design (N. Munro, ed.), pp. 339-352. The Institution of Electrical Engineers, London, England, 1999.
5. Horner, W. G.: Philos. Trans. Royal Soc. London 109, 308-335 (1819).
6. IEEE. IEEE Standard for binary floating-point arithmetic. Technical Report IEEE Std 754-1985, 1985. Reaffirmed 1990.
7. Moore, R.E.: Interval analysis. Englewood Cliffs, NJ: Prentice-Hall 1966.
8. Shih-Chieh, C.: Precious mirror of the four elements, 1303.
9. Stahl, V.: Interval methods for bounding the range of polynomials and solving systems of nonlinear equations. PhD thesis, University of Linz, Austria, 1995.