Algorithmisches Differenzieren - M1
Algorithmisches Differenzieren - M1 Algorithmisches Differenzieren - M1
REFERENCES 25 [30] Cuyt, A.A.M., Rall, L.B.: Computational implementation of the multivariate Halley method for solving nonlinear systems of equations. ACM Transactions on Mathematical Software 11, 1985, 20-36. [31] Davis, P.H., Pryce, J.D.: A New Implementation of Automatic Differentiation for Use with Numerical Software. Technical Report AM-87-11, School of Mathematics, University of Bristol, 1987. [32] Davis, P.H., Pryce, J.D., Stephens, B.: Recent developments in automatic differentiation. In: Scientific Software Systems, ed. by J.C.Mason and M.G.Cox, Chapman and Hall, London, 1990, 153-165. [33] Davis, P.H., Stephens, B., Corliss, G.F., Krenz, G.S.: Specification of a Preprocessor for Use with Differentiation Arithmetic. Technical Report AM-88-08, School of Mathematics, University of Bristol, 1988. [34] Dixon, L.C.W.: Automatic differentiation and parallel processing in optimisation. In: Optimization, Parallel Processing and Applications, ed. by A.Kurzhanski, K.Neumann, D.Pallaschke, (Lecture Notes in Economics and Mathematical Systems 304), Springer-Verlag, Berlin, 1988, 86-93. [35] Dixon, L.C.W.: On the impact of automatic differentiation on the relative performance of parallel truncated Newton and variable metric algorithms. SIAM Journal on Optimization 1, 1991, 475-486. [36] Dixon, L.C.W.: Use of automatic differentiation for calculating Hessians and Newton steps. In [70], 114-125. [37] Dixon, L.C.W., Maany, Z., Mohseninia, M.: Finite Element Optimisation in ADA using Automatic Differentiation. Technical Report 205, Numerical Optimisation Centre, Hatfield Polytechnic, 1988. [38] Dixon, L.C.W., Maany, Z., Mohseninia, M.: Automatic differentiation of large sparse systems. Journal of Economic Dynamics and Control 14, 1990, 299-311. [39] Dixon, L.C.W., Price, R.C.: Truncated Newton method for sparse unconstrained optimization using automatic differentiation. Journal of Optimization Theory and Applications 60, 1989, 261-275. [40] Evtushenko, Yu.G.: Automatic differentiation viewed from optimal control theory. In [70], 25-30. [41] Fischer, H.: Some aspects of automatic differentiation. In: Numerical Methods and Approximation Theory III, ed. by G.V. Milovanović, University of Niˇs, Yugoslavia, 1988, 199-208. [42] Fischer, H.: Automatic differentiation: Fast method to compute the quadratic form of Hessian matrix and given vector. Facta Universitatis (Niˇs), Ser.Math.Inform.3, 1988, 51-59.
REFERENCES 26 [43] Fischer, H.: Automatic differentiation of characterizing sequences. Journal of Computational and Applied Mathematics 28, 1989, 181-185. [44] Fischer, H.: Fast method to compute the scalar product of gradient and given vector. Computing 41, 1989, 261-265. [45] Fischer, H.: Automatic differentiation: Parallel computation of function, gradient, and Hessian matrix. Parallel Computing 13, 1990, 101-110. [46] Fischer, H.: Automatic and parallel generation of gradient and Hessian matrix. In: System Modelling and Optimization, ed. by H.J.Sebastian and K.Tammer, (Lecture Notes in Control and Information Sciences 143), Springer-Verlag, Berlin, 1990, 104-114. [47] Fischer, H.: Automatic differentiation of the vector that solves a parametric linear system. Journal of Computational and Applied Mathematics 35, 1991, 169-184. [48] Fischer, H.: Special problems in automatic differentiation. In [70], 43-50. [49] Fischer, H.: Automatic differentiation: Reduced gradient and reduced Hessian matrix. Computational Optimization and Applications 1, 1992, 327-344. [50] Fischer, H.: Automatisches Differenzieren. In: Wissenschaftliches Rechnen - Eine Einführung in das Scientific Computing. edited by J.Herzberger, Akademie- Verlag, Berlin, 1995, 53-104. [51] Fischer, H.: Automatic differentiation: The key idea and an illustrative example. In: Applied Mathematics and Parallel Computing, edited by H.Fischer, B.Riedmüller, S.Schäffler, Physica-Verlag, Heidelberg, 1996, 121–139. [52] Automatic Differentiation: Root Problem and Branch Problem. In: Encyclopedia of Optimization, Kluwer Academic Publishers, 2001, edited by C.A.Floudas, P.M.Pardalos. [53] Algorithmic Differentiation with Intervals. In: Inclusion Methods for Nonlinear Problems, with Applications in Engineering, Economics and Physics, edited by J.Herzberger, Springer-Verlag, Computing Supplementum 16, 2002, 45–65. [54] Fischer, H., Flanders, H.: A minimal code list. Theoretical Computer Science 215, 1999, 345–348. [55] Fischer, H., Hertneck, Ch.: Gradient and Hessian matrix forward with functions version A in ANSI-C. Technical Report IAMS1995.8TUM, Institut für Angewandte Mathematik und Statistik, Technische Universität München, 1995. [56] Fischer, H., Schäffler, S., Warsitz, H.: Parameter estimation in linear regression models with stationary ARMA(p,q)-errors using automatic differentiation. Yugoslav Journal of Operations Research 2, 1992, 55-68. [57] Fischer, H., Warsitz, H.: Complexity of derivatives generated by symbolic differentiation. In: Computer Algebra in Scientific Computing, Proceedings of the Third Workshop on Computer Algebra in Scientific Computing, CASC-2000, Samarkand, October 5–9, 2000, ed. by V.G.Ganzha, E.W.Mayr, E.V.Vorozhtsov, Springer-Verlag, 2000, 129–144.
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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
- Seite 7 und 8: 2 VORWÄRTS-METHODE 6 Beispiel 1 Ge
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- Seite 11 und 12: 2 VORWÄRTS-METHODE 10 Damit ergibt
- Seite 13 und 14: 2 VORWÄRTS-METHODE 12 Wir definier
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- 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 und 24: 3 RÜCKWÄRTS-METHODE 22 Schließli
- Seite 25: REFERENCES 24 [16] Bischof, Ch., Ca
- 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
REFERENCES 26<br />
[43] Fischer, H.: Automatic differentiation of characterizing sequences. Journal of<br />
Computational and Applied Mathematics 28, 1989, 181-185.<br />
[44] Fischer, H.: Fast method to compute the scalar product of gradient and given<br />
vector. Computing 41, 1989, 261-265.<br />
[45] Fischer, H.: Automatic differentiation: Parallel computation of function, gradient,<br />
and Hessian matrix. Parallel Computing 13, 1990, 101-110.<br />
[46] Fischer, H.: Automatic and parallel generation of gradient and Hessian matrix.<br />
In: System Modelling and Optimization, ed. by H.J.Sebastian and K.Tammer,<br />
(Lecture Notes in Control and Information Sciences 143), Springer-Verlag, Berlin,<br />
1990, 104-114.<br />
[47] Fischer, H.: Automatic differentiation of the vector that solves a parametric linear<br />
system. Journal of Computational and Applied Mathematics 35, 1991, 169-184.<br />
[48] Fischer, H.: Special problems in automatic differentiation. In [70], 43-50.<br />
[49] Fischer, H.: Automatic differentiation: Reduced gradient and reduced Hessian<br />
matrix. Computational Optimization and Applications 1, 1992, 327-344.<br />
[50] Fischer, H.: Automatisches <strong>Differenzieren</strong>. In: Wissenschaftliches Rechnen -<br />
Eine Einführung in das Scientific Computing. edited by J.Herzberger, Akademie-<br />
Verlag, Berlin, 1995, 53-104.<br />
[51] Fischer, H.: Automatic differentiation: The key idea and an illustrative example.<br />
In: Applied Mathematics and Parallel Computing, edited by H.Fischer,<br />
B.Riedmüller, S.Schäffler, Physica-Verlag, Heidelberg, 1996, 121–139.<br />
[52] Automatic Differentiation: Root Problem and Branch Problem. In: Encyclopedia<br />
of Optimization, Kluwer Academic Publishers, 2001, edited by C.A.Floudas,<br />
P.M.Pardalos.<br />
[53] Algorithmic Differentiation with Intervals. In: Inclusion Methods for Nonlinear<br />
Problems, with Applications in Engineering, Economics and Physics, edited by<br />
J.Herzberger, Springer-Verlag, Computing Supplementum 16, 2002, 45–65.<br />
[54] Fischer, H., Flanders, H.: A minimal code list. Theoretical Computer Science<br />
215, 1999, 345–348.<br />
[55] Fischer, H., Hertneck, Ch.: Gradient and Hessian matrix forward with functions<br />
version A in ANSI-C. Technical Report IAMS1995.8TUM, Institut für Angewandte<br />
Mathematik und Statistik, Technische Universität München, 1995.<br />
[56] Fischer, H., Schäffler, S., Warsitz, H.: Parameter estimation in linear regression<br />
models with stationary ARMA(p,q)-errors using automatic differentiation.<br />
Yugoslav Journal of Operations Research 2, 1992, 55-68.<br />
[57] Fischer, H., Warsitz, H.: Complexity of derivatives generated by symbolic differentiation.<br />
In: Computer Algebra in Scientific Computing, Proceedings of the<br />
Third Workshop on Computer Algebra in Scientific Computing, CASC-2000,<br />
Samarkand, October 5–9, 2000, ed. by V.G.Ganzha, E.W.Mayr, E.V.Vorozhtsov,<br />
Springer-Verlag, 2000, 129–144.
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