Algorithmisches Differenzieren - M1

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$Prof. Dr. Bastian von Harrach Dipl. Math. Marcel Ullrich ... - M1$

REFERENCES 23 References [1] Aberth, O.: Precise Numerical Analysis. William C.Brown Publishers, Dubuque, Iowa, USA, 1988. [2] Aida-Zade, K.R., Evtushenko, Yu.G.: Bystroe avtomaticheskoe differentsirovanie na EVM. Matematicheskoe Modelirovanie 1, 1989, 120-131. [3] Arbenz, P., Gander, W.: Solving nonlinear eigenvalue problems by algorithmic differentiation. Computing 36, 1986, 205-215. [4] Bartholomew-Biggs, M.C., Bartholomew-Biggs, L., Christianson, B.: Optimization and Automatic Differentiation in Ada: Some practical experience. Optimization Methods and Software 4, 1994, 47-73. [5] Barton, D.: On Taylor series and stiff equations. ACM Transactions on Mathematical Software 6, 1980, 280-294. [6] Barton, D., Willers, I.M., Zahar, R.V.M.: Taylor series methods for ordinary differential equations - an evaluation. In: Mathematical Software, ed. by J.Rice, Academic Press, New York, 1971, 369-390. [7] Baur, W., Strassen, V.: The complexity of partial derivatives. Theoretical Computer Science 22, 1983, 317-330. [8] Beck, T.: Automatisches <strong>Differenzieren</strong> von Algorithmen. Dissertation, Technische Universität München, 1991. [9] Beck, T.: Automatic differentiation of iterative processes. Journal of Computational and Applied Mathematics 50, 1994, 109-118. [10] Beck, T., Fischer, H.: The if-problem in automatic differentiation. Journal of Computational and Applied Mathematics 50, 1994, 119-131. [11] Beda, L.M., Korolev, L.N., Sukkikh, N.V., Frolova, T.S.: Programme zum Automatischen <strong>Differenzieren</strong> für die Maschine BESM, (in Russisch). Technischer Bericht, Akademie der Wissenschaften der UdSSR, Moskau, 1959. [12] Berz, M.: Differential algebra - A new tool. In: Proceedings of the 1989 IEEE Particle Accelerator Conference, March 20-23, 1989, ed. by F.Bennet and J.Kopta, IEEE, 1989. [13] Berz, M.: Forward algorithms for higher derivatives in many variables with applications to beam physics. In [70], 147-156. [14] Berz, M.: Automatic differentiation as nonarchimedean analysis. In: Computer Arithmetic and Enclosure Methods, ed. by L.Atanassova and J.Herzberger, Elsevier (North-Holland), Amsterdam, 1992, 439-450. [15] Bischof, Ch.H.: Issues in parallel automatic differentiation. In [70], 100-113.
REFERENCES 24 [16] Bischof, Ch., Carle, A., Corliss, G.F., Griewank, A.: ADIFOR: Automatic differentiation in a source translator environment. Preprint MCS-P288-0192, Argonne National Laboratory, 1992. [17] Bischof, Ch., Griewank, A.: ADIFOR: A Fortran system for portable automatic differentiation. Preprint MCS-P317-0792, Argonne National Laboratory, 1992. [18] Bischof, Ch., Griewank, A., Juedes, D.: Exploiting parallelism in automatic differentiation. In: Proceedings of the 1991 International Conference on Supercomputing, ed. by E.Houstis and Y.Muraoka, ACM Press, 1991, 146-153. [19] Bohlender, G., Rall, L.B., Ullrich, Ch., Wolff von Gudenberg, J.: PASCAL- SC: Wirkungsvoll programmieren, kontrolliert rechnen. Bibliographisches Institut, Zürich, 1986. [20] Carlile, B.R.: Solution of nonlinear systems of equations on the FPS 64-bit family of scientific computers using automatic differentiation. In: Proceedings of the 1986 Array Conference, Portland, Oregon, 1986, 142-169. [21] Christianson, B.: Automatic Hessians by reverse accumulation. IMA Journal of Numerical Analysis 12, 1992, 135-150. [22] Christianson, B.: Reverse accumulation and accurate rounding error estimates for Taylor series coefficients. Optimization Methods and Software 1, 1992, 81-94. [23] Christianson, B.: Reverse accumulation and attractive fixed points. Optimization Methods and Software 3, 1994, 311-326. [24] Corliss, G.F.: Computing narrow inclusions for definite integrals. In: Computerarithmetic, Scientific Computation and Programming Languages, ed. by E.Kaucher, U.Kulisch, Ch.Ullrich, Teubner-Verlag, Stuttgart, 1987, 150-169. [25] Corliss, G.F.: Applications of differentiation arithmetic. In: Reliability in Computing: The Role of Interval Methods in Scientific Computing, ed. by R.E.Moore, Academic Press, London, 1988, 127-148. [26] Corliss, G.F.: Overloading point and interval Taylor operators. In [70], 139-146. [27] Corliss, G.F., Chang, Y.F.: Solving ordinary differential equations using Taylor series. ACM Transactions on Mathematical Software 8, 1982, 114-144. [28] Corliss, G., Rall, L.B.: Automatic generation of Taylor series in PASCAL-SC: Basic operations and applications to ordinary differential equations. In: Transactions of the First Army Conference on Applied Mathematics and Computing, U.S. Army Research Office, Research Triangle Park, NC, 1984, 177-209. [29] Corliss, G., Rall, L.B.: Adaptive, self-validating numerical quadrature. SIAM Journal on Scientific and Statistical Computing 8, 1987, 831-847.
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Seite 3 und 4: 1 EINLEITUNG 2 Es ist klar, daß in
Seite 5 und 6: 2 VORWÄRTS-METHODE 4 2 Vorwärts-M
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Seite 13 und 14: 2 VORWÄRTS-METHODE 12 Wir definier
Seite 15 und 16: 3 RÜCKWÄRTS-METHODE 14 3 Rückwä
Seite 17 und 18: 3 RÜCKWÄRTS-METHODE 16 (1) Berech
Seite 19 und 20: 3 RÜCKWÄRTS-METHODE 18 Tk yk ¯yk
Seite 21 und 22: 3 RÜCKWÄRTS-METHODE 20 Wir defini
Seite 23: 3 RÜCKWÄRTS-METHODE 22 Schließli
Seite 27 und 28: REFERENCES 26 [43] Fischer, H.: Aut
Seite 29 und 30: REFERENCES 28 [73] Hillstrom, K.E.:
Seite 31 und 32: REFERENCES 30 [104] Liepelt, M., Sc
Seite 33: REFERENCES 32 [134] Shiriaev, D.: F

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