| Title:
|
Practical aspects of interval computation (English) |
| Author:
|
Moore, Ramon E. |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
13 |
| Issue:
|
1 |
| Year:
|
1968 |
| Pages:
|
52-92 |
| . |
| Category:
|
math |
| . |
| Keyword:
|
numerical analysis |
| idZBL:
|
Zbl 0184.37401 |
| DOI:
|
10.21136/AM.1968.103139 |
| . |
| Date available:
|
2008-05-20T17:41:06Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103139 |
| . |
| Reference:
|
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| Reference:
|
[2] Apostolatos N., Kulisch U.: Grundlagen einer Maschinenintervallarithmetik.Technische Hochschule Karlsruhe, Karlsruhe, September, 1966. MR 0239720 |
| Reference:
|
[3] Apostolatos N., Kulisch U.: Approximation der erweiterten Intervallarithmetik durch die einfache Maschinenintervallarithmetik.THK, Karlsruhe, November, 1966. MR 0239721 |
| Reference:
|
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[6] Babuška I., Práger M., and Vitásek E.: Numerical Processes in Differential Equations.Interscience, London, 1966. MR 0223101 |
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| Reference:
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| Reference:
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[12] Collins G.: PM, a system for polynomial manipulation.Comm. A.C.M., Vol. 9, No. 8, August, 1966, pp. 578 - 589. (See also other papers in this same issue.) Zbl 0152.15803 |
| Reference:
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[13] Dahlquist G.: On rigorous error bounds in the numerical solutions of ordinary differential equations.Numerical Solutions of Nonlinear Differential Equations, Ed. by D. Greenspan, Wiley, 1966, pp. 89-96. MR 0208838 |
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[14] Dargel R. H., Loscalzo F. R., and Witt T. H.: Automatic Error Bounds on Real Zeros of Rational Functions.Communications of the ACM, Vol. P, No. 11, 1966, pp. 806-809. 10.1145/365876.365913 |
| Reference:
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[15] Fehlberg E.: Eine Methode zur Fehlerverkleinerung beim Runge-Kutta-Verfahren.Z. Angew. Math. Mech., 38 (1958), pp. 421 - 426. Zbl 0085.11002, MR 0100358, 10.1002/zamm.19580381102 |
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[16] Fehlberg E.: Runge-Kutta type formulas of high order accuracy and their application to the numerical integration of the restricted problem of three bodies.Proc. Int. Symp. on Analogue and Digital Techniques Applied to Aeronautics, Liege, Belgium, September, 1963. |
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[17] Fehlberg E.: Zur numerische Integration von Differential-gleichungen durch Potenzreihen-Ansätze....Z. Angew. Math. Mech., 44 (1964), pp. 83-88. MR 0177507, 10.1002/zamm.19640440303 |
| Reference:
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[18] Fehlberg E.: New High-Order Runge-Kutta Formulas with Step-size Control for Systems of First-and Second-Order Differential Equations.Z. Angew. Math. Mech., 44 (1964), Sonderheft, pp. T17-T29. Zbl 0137.33105, MR 0185826, 10.1002/zamm.19640441310 |
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[19] Fehlberg E.: New High-order Runge Kutta Formulas with an Arbitrarily Small Truncation Error.(personal communication), 1965. MR 0193755 |
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[21] Gallaher L. J., Perlin I. E.: A comparison of several methods of numerical integration of nonlinear differential equations.RECC, Georgia Institute of Technology, Atlanta, Georgia, 1966. |
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[24] Goldstine H. H., Von Neumann J.: Numerical inverting of matrices of high order, II.Proc. Amer. Math. Soc., Vol. 2, 1951, pp. 199-202. Also: Bull. Amer. Math. Soc. 53 (1947) pp. 1021-1099. Zbl 0043.12301, MR 0024235 |
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[25] Gröbner W.: Die Lie Reihen und Ihre Anwendungen.Deutscher Verlag der Wissenschaften, Berlin, 1960. MR 0116102 |
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[26] Hansen E.: Interval arithmetic in matrix computations.J.S.I.A.M., series B, Numerical Analysis, Part 1, 2 (1965), pp. 308-320. Zbl 0135.37303, MR 0187381 |
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[27] Hansen E., Smith R.: Interval arithmetic in matrix computations, Part 2.J.S.I.A.M., series B, Numerical Analysis, 4: 1 (1967), pp. 1 - 9. MR 0229372 |
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[29] Henrici P.: Discrete Variable Methods in Ordinary Differential Equations.Wiley, New York, 1962. Zbl 0112.34901, MR 0135729 |
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[34] Moore R. E.: The automatic analysis and control of error in digital computation based on the use of interval numbers.Error in Digital Computation, Vol. I, Ed. by L. B. Rall, Wiley, 1965, pp. 61-130. Zbl 0202.45002, MR 0176614 |
| Reference:
|
[35] Moore R. E.: Automatic local coordinate transformations to reduce the growth of error bounds in interval computation of solutions of ordinary differential equations.Error in Digital Computation, Vol. II, Ed. by L. B. Rall, Wiley, New York, 1965, pp. 103-140. Zbl 0202.45101, MR 0185839 |
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|
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| . |
