Algorithmisches Differenzieren - M1
Algorithmisches Differenzieren - M1 Algorithmisches Differenzieren - M1
REFERENCES 31 [120] Rall, L.B.: Applications of software for automatic differentiation in numerical computation. In: Fundamentals of Numerical Computation, ed. by G.Alefeld and R.D.Grigorieff, (Computing Supplementum 2), Springer-Verlag, Wien, 1980, 141-156. [121] Rall, L.B.: Automatic Differentiation: Techniques and Applications. (Lecture Notes in Computer Science 120), Springer-Verlag, Berlin, 1981. [122] Rall, L.B.: Differentiation and generation of Taylor-coefficients in PASCAL- SC. In: A New Approach to Scientific Computation, ed. by U.Kulisch and W.L.Miranker, Academic Press, New York, 1983, 291-309. [123] Rall, L.B.: Differentiation in PASCAL-SC: type GRADIENT. ACM Transactions on Mathematical Software 10, 1984, 161-184. [124] Rall, L.B.: Global optimization using automatic differentiation and interval iteration. Technical Summary Report 2832, Mathematics Research Center, University of Wisconsin, Madison, 1985. [125] Rall, L.B.: Improved interval bounds for ranges of functions. In: Interval Mathematics 1985, ed. by K.Nickel, (Lecture Notes in Computer Science 212), Springer- Verlag, Berlin, 1986, 143-155. [126] Rall, L.B.: Optimal implementation of differentiation arithmetic. In: Computerarithmetic, Scientific Computation and Programming Languages, ed. by E.Kaucher, U.Kulisch, Ch.Ullrich, Teubner-Verlag, Stuttgart, 1987, 287-295. [127] Rall, L.B.: Differentiation arithmetics. In: Computer Arithmetic and Self- Validating Numerical Methods, ed. by Ch.Ullrich, (Notes and Reports in Mathematics in Science and Engineering, Vol.7), Academic Press, New York, 1990, 73-90. [128] Rall, L.B.: Point and interval differentiation arithmetics. In [70], 17-24. [129] Rich, L.C., Hill, D.R.: Automatic differentiation in MATLAB. Applied Numerical Mathematics 9, 1992, 33-43. [130] Rosemblun, M.: Automatic Differentiation: Overview and Application to Systems of Parametrized Nonlinear Equations. Technical Report CRPC-TR92262, Center for Research on Parallel Computation, Rice University, 1992. [131] Saarinen, S., Bramley, R.B., Cybenko, G.: Neural networks, backpropagation, and automatic differentiation. In [70], 31-42. [132] Sawyer, J.W.: First partial differentiation by computer with an application to categorial data analysis. The American Statistician 38, 1984, 300-308. [133] Shiriaev, D.: Reduction of spatial complexity in reverse automatic differentiation by means of inverted code. In: Computer Arithmetic and Enclosure Methods, ed. by L.Atanassova and J.Herzberger, Elsevier (North-Holland), Amsterdam, 1992, 475-484.
REFERENCES 32 [134] Shiriaev, D.: Fast Automatic Differentiation for Vector Processors and Reduction of the Spatial Complexity in a Source Translation Environment. Dissertation, Universität Karlsruhe, 1993. [135] Soulié, E.J.: User’s experience with FORTRAN compilers in least squares problems. In [70], 297-306. [136] Speelpenning, B.: Compiling fast partial derivatives of functions given by algorithms. Ph.D.Thesis, Department of Computer Science, University of Illinois, Urbana-Champaign, 1980. [137] Stephens, B.R., Pryce, J.D.: DAPRE, A Differentiation Arithmetic System for FORTRAN. Technical Report ACM-91-3, Royal Military College of Science, Shrivenham, UK, 1991. [138] Tesfatsion, L.: Automatic evaluation of higher-order partial derivatives for nonlocal sensitivity analysis. In [70], 157-165. [139] Thacker, W.C.: Automatic differentiation from an oceanographer’s perspective. In [70], 191-201. [140] van den Heuvel, P., van Hulzen, J.A., Goldmann, V.V.: Automatic generation of FORTRAN-coded Jacobians and Hessians. In: Proceedings of EUROCAL 87, ed. by J.Davenport, (Lecture Notes in Computer Science 378), Springer-Verlag, Berlin, 1987, 120-131. [141] Van Iwaarden, R.: Automatic differentiation applied to unconstrained nonlinear optimization with result verification. Interval Computations, No.3, 1993, 41-60. [142] Volin, Yu.M., Ostrovskii, G.M.: Automatic computation of derivatives with the use of the multilevel differentiation technique - 1. Algorithmic basis. Computers and Mathematics with Applications 11, 1985, 1099-1114. [143] Warner, D.D.: A partial derivative generator. Computing Science Technical Report No.28, Bell Telephone Laboratories, Murray Hill, N.J., 1975. [144] Wexler, A.: Automatic evaluation of derivatives. Applied Mathematics and Computation 24, 1987, 19-46. [145] Wexler, A.: An algorithm for exact evaluation of multivariate functions and their derivatives to any order. Computational Statistics and Data Analysis 6, 1988, 1-6. file vorlesung123.tex
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REFERENCES 31<br />
[120] Rall, L.B.: Applications of software for automatic differentiation in numerical<br />
computation. In: Fundamentals of Numerical Computation, ed. by G.Alefeld<br />
and R.D.Grigorieff, (Computing Supplementum 2), Springer-Verlag, Wien, 1980,<br />
141-156.<br />
[121] Rall, L.B.: Automatic Differentiation: Techniques and Applications. (Lecture<br />
Notes in Computer Science 120), Springer-Verlag, Berlin, 1981.<br />
[122] Rall, L.B.: Differentiation and generation of Taylor-coefficients in PASCAL-<br />
SC. In: A New Approach to Scientific Computation, ed. by U.Kulisch and<br />
W.L.Miranker, Academic Press, New York, 1983, 291-309.<br />
[123] Rall, L.B.: Differentiation in PASCAL-SC: type GRADIENT. ACM Transactions<br />
on Mathematical Software 10, 1984, 161-184.<br />
[124] Rall, L.B.: Global optimization using automatic differentiation and interval iteration.<br />
Technical Summary Report 2832, Mathematics Research Center, University<br />
of Wisconsin, Madison, 1985.<br />
[125] Rall, L.B.: Improved interval bounds for ranges of functions. In: Interval Mathematics<br />
1985, ed. by K.Nickel, (Lecture Notes in Computer Science 212), Springer-<br />
Verlag, Berlin, 1986, 143-155.<br />
[126] Rall, L.B.: Optimal implementation of differentiation arithmetic. In: Computerarithmetic,<br />
Scientific Computation and Programming Languages, ed. by<br />
E.Kaucher, U.Kulisch, Ch.Ullrich, Teubner-Verlag, Stuttgart, 1987, 287-295.<br />
[127] Rall, L.B.: Differentiation arithmetics. In: Computer Arithmetic and Self-<br />
Validating Numerical Methods, ed. by Ch.Ullrich, (Notes and Reports in Mathematics<br />
in Science and Engineering, Vol.7), Academic Press, New York, 1990,<br />
73-90.<br />
[128] Rall, L.B.: Point and interval differentiation arithmetics. In [70], 17-24.<br />
[129] Rich, L.C., Hill, D.R.: Automatic differentiation in MATLAB. Applied Numerical<br />
Mathematics 9, 1992, 33-43.<br />
[130] Rosemblun, M.: Automatic Differentiation: Overview and Application to Systems<br />
of Parametrized Nonlinear Equations. Technical Report CRPC-TR92262,<br />
Center for Research on Parallel Computation, Rice University, 1992.<br />
[131] Saarinen, S., Bramley, R.B., Cybenko, G.: Neural networks, backpropagation,<br />
and automatic differentiation. In [70], 31-42.<br />
[132] Sawyer, J.W.: First partial differentiation by computer with an application to<br />
categorial data analysis. The American Statistician 38, 1984, 300-308.<br />
[133] Shiriaev, D.: Reduction of spatial complexity in reverse automatic differentiation<br />
by means of inverted code. In: Computer Arithmetic and Enclosure Methods, ed.<br />
by L.Atanassova and J.Herzberger, Elsevier (North-Holland), Amsterdam, 1992,<br />
475-484.
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