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Keywords:
numerical analysis
References:
[1] Anselone P. M.: Convergence and error bounds for approximate solutions of integral and operator equations. Error in Digital Computation, Vol. II, Ed. by L. B. Rall, Wiley, New York, 1965, pp. 219-230. MR 0189277 | Zbl 0158.34102
[2] Apostolatos N., Kulisch U.: Grundlagen einer Maschinenintervallarithmetik. Technische Hochschule Karlsruhe, Karlsruhe, September, 1966. MR 0239720
[3] Apostolatos N., Kulisch U.: Approximation der erweiterten Intervallarithmetik durch die einfache Maschinenintervallarithmetik. THK, Karlsruhe, November, 1966. MR 0239721
[4] Apostolatos N., Kulisch U., and Nickel K.: Ein Einschliessungsverfahren für Nullstellen. THK, Karlsruhe, December, 1966. MR 0229380
[5] Babuška I., Sobolev S. L.: Оптимизация численных методов. Aplikace matematiky, svazek 10 (1965), pp. 96-129. MR 0191072
[6] Babuška I., Práger M., and Vitásek E.: Numerical Processes in Differential Equations. Interscience, London, 1966. MR 0223101
[7] Banach S.: Opérations Linéaires. Monografje Matematyczne, Warsaw, 1932. Zbl 0005.20901
[8] Boche R.: Complex interval arithmetic with some applications. Lockheed Missiles and Space Company report # 4-22-61-1, 1966.
[9] Brown R. W.: Upper and lower bounds for solutions of integral equations. Error in Digital Computation, Vol. II, Ed. by L. B. Rall, Wiley, New York, 1965, pp. 231 - 252.
[10] Collatz L.: Numerical Treatment of Differential Equations. (English Ed.), Berlin, 1959.
[11] Collatz L.: Applications of functional analysis to error estimation. Error in Digital Computation, Vol. II, Ed. by L. B. Rall, Wiley, New York, 1965, pp. 253-269. Zbl 0163.38603
[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
[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
[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. DOI 10.1145/365876.365913
[15] Fehlberg E.: Eine Methode zur Fehlerverkleinerung beim Runge-Kutta-Verfahren. Z. Angew. Math. Mech., 38 (1958), pp. 421 - 426. DOI 10.1002/zamm.19580381102 | MR 0100358 | Zbl 0085.11002
[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.
[17] Fehlberg E.: Zur numerische Integration von Differential-gleichungen durch Potenzreihen-Ansätze... Z. Angew. Math. Mech., 44 (1964), pp. 83-88. DOI 10.1002/zamm.19640440303 | MR 0177507
[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. MR 0185826 | Zbl 0137.33105
[19] Fehlberg E.: New High-order Runge Kutta Formulas with an Arbitrarily Small Truncation Error. (personal communication), 1965. MR 0193755
[20] Fréchet M.: Les Espaces Abstraits. Gauthier-Villars, Paris, 1928.
[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.
[22] Gibb A.: ALGOL 60 Procedures for Range Arithmetic. Tech. Rep. No. 10, Appl. Math. Stat. Lab., Stanford University, 1961.
[23] Gingerich O.: The Computer Versus Kepler. American Scientist, 52, 1964, pp. 218-226.
[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. MR 0024235 | Zbl 0043.12301
[25] Gröbner W.: Die Lie Reihen und Ihre Anwendungen. Deutscher Verlag der Wissenschaften, Berlin, 1960. MR 0116102
[26] Hansen E.: Interval arithmetic in matrix computations. J.S.I.A.M., series B, Numerical Analysis, Part 1, 2 (1965), pp. 308-320. MR 0187381 | Zbl 0135.37303
[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
[28] Hansen E.: On solving systems of equations using interval arithmetic. (to appear). MR 0229411 | Zbl 0223.65012
[29] Henrici P.: Discrete Variable Methods in Ordinary Differential Equations. Wiley, New York, 1962. MR 0135729 | Zbl 0112.34901
[30] Kantorovič L. V.: On Newton's method for functional equations. Dokl. Akad. Nauk SSSR (N.S.), 59 (1948), pp. 1237-1240. MR 0024700
[31] Krückeberg F.: Zur numerische Intervallrechnung. Rheinisch-Westfälisches Institute für Instrumentelle Mathematik, Bonn, June, 1966.
[32] Krückeberg F.: Defekterfassung bei gewöhnlichen und partiellen Differentialgleichungen. Bonn, June, 1966.
[33] Meinguet J.: La controle des erreurs en calcul automatique. M.B.L.E. Laboratoire des Recherches, Brussels, Rapport R 29, avril, 1965.
[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. MR 0176614 | Zbl 0202.45002
[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. MR 0185839 | Zbl 0202.45101
[36] Moore R. E.: Interval Analysis. Prentice-Hall, 1966. MR 0231516 | Zbl 0176.13301
[37] von Neumann J., Goldstine H.: Numerical Inversion of Matrices of High Order. Bulletin of Amer. Math. Soc. 53 (1947).
[38] Rall L. B.: Computational Methods for Nonlinear Operator Equations. (to appear).
[39] Reiter A.: Compiler of differentiable expressions. MRC Computer Program #1., Mathematics Research Center, University of Wisconsin.
[40] Reiter A.: Interval arithmetic package. MRC Computer Program #2, Math. Res. Center, University of Wisconsin.
[41] Turing A. M.: Rounding-off errors in matrix processes. Quart. J. Mech. Appl. Math., Vol. 1, 1948, pp. 287-308. DOI 10.1093/qjmam/1.1.287 | MR 0028100 | Zbl 0033.28501
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