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Books on the topic 'Approximation of derivatives of functions'

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Published: 5 June 2025

Last updated: 16 July 2025

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1

Temli͡akov, V. N. Approximation of functions with bounded mixed derivative. American Mathematical Society, 1989.

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2

Alyukov, Sergey. Approximation of piecewise linear and generalized functions. INFRA-M Academic Publishing LLC., 2024. http://dx.doi.org/10.12737/2104876.

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The monograph is devoted to piecewise linear and generalized functions. They are widely used in various fields of research: in the theory of signal transmission and transformation, quantum field theory, control theory, problems of nonlinear dynamics, structural mechanics, semiconductor theory, economic applications, medicine, description of impulse effects and many others. When creating mathematical models, in some cases it is necessary to approximate these functions using analytical expressions, but not in the form of linear combinations, as in known methods, but in the form of attachments, compositions, using recursive sequences. The considered methods are devoid of the disadvantages of Fourier series and have advantages over other approximation methods. The developed approximation methods help to understand the meaning and content of generalized functions and their derivatives, and contribute to the conscious application of these functions in mathematical modeling problems. These methods can be used in a wide range of applied research, from medicine to quantum electronics. The theoretical material is illustrated by a large number of practical examples from a wide variety of applied fields. The fundamentals of the developed macroeconomic theory with impulse, shock, spasmodic characteristics and other types of rapidly changing processes are presented. For mathematicians, students and teachers, and specialists working in applied research fields.

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3

Nürnberger, Günther. Approximation by Spline Functions. Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-61342-5.

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4

Temli͡akov, V. N. Approximation of periodic functions. Nova Science Publishers, 1993.

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5

Nürnberger, G. Approximation by spline functions. Springer-Verlag, 1989.

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6

Temli︠a︡kov, V. N. Approximation of periodic functions. Nova Science Publishers, 1993.

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7

Mashreghi, Javad. Derivatives of Inner Functions. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-5611-7.

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8

Mashreghi, Javad. Derivatives of Inner Functions. Springer New York, 2013.

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9

Petrushev, P. P. Rational approximation of real functions. Cambridge University Press, 1987.

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10

Stepanet͡s, A. I. Classification and approximation of periodic functions. Kluwer Academic Publishers, 1995.

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11

Trigub, Roald M., and Eduard S. Bellinsky. Fourier Analysis and Approximation of Functions. Springer Netherlands, 2004. http://dx.doi.org/10.1007/978-1-4020-2876-2.

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12

Singh, S. P., ed. Approximation Theory, Spline Functions and Applications. Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-011-2634-2.

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13

Stepanets, Alexander I. Classification and Approximation of Periodic Functions. Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-011-0115-8.

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14

Danmarks tekniske højskole. Numerisk institut., ed. Minimization of non-linear approximation functions. Institute for Numerical Analysis, Technical University of Denmark, 1985.

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15

S, Belinsky Eduard, ed. Fourier analysis and approximation of functions. Kluwer Academic Publishers, 2004.

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16

1937-, Singh S. P., and North Atlantic Treaty Organization. Scientific Affairs Division., eds. Approximation theory, spline functions, and applications. Kluwer Academic Publishers, 1992.

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17

Guzman, Alberto. Derivatives and Integrals of Multivariable Functions. Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-1-4612-0035-2.

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18

1947-, Guzman Alberto. Derivatives and integrals of multivariable functions. Birkhauser, 2003.

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19

1948-, Nürnberger G., Schmidt Jochen W, and Walz Guido, eds. Multivariate approximation and splines. Birkhäuser, 1997.

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20

Brent, R. P. Algorithms for minimization without derivatives. Dover Publications, 2002.

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21

Gaier, Dieter. Lectures on complex approximation. Birkhäuser, 1987.

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22

Bucur, Ileana, and Gavriil Paltineanu. Topics in Uniform Approximation of Continuous Functions. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-48412-5.

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23

Rivlin, Theodore J. An introduction to the approximation of functions. Dover Publications, 2003.

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24

K, Chui C., Schumaker Larry L. 1939-, and Utreras Florencio I, eds. Topics in multivariate approximation. Academic Press, 1987.

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25

Kitahara, Kazuaki. Spaces of approximating functions with Haar-like conditions. Springer-Verlag, 1994.

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26

Milovanović, Gradimir V., and Michael Th Rassias, eds. Analytic Number Theory, Approximation Theory, and Special Functions. Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4939-0258-3.

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27

A, Shevchuk Igor, ed. Theory of uniform approximation of functions by polynomials. Walter De Gruyter, 2008.

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28

McCormick, S. Thomas. Easy with difficulty objective functions for Max cut. Indian Institute of Management, 2002.

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29

Murty, Vijaya Kumar. Non-vanishing of L-functions and their derivatives. Dept. of Mathematics, University of Toronto, 1989.

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30

Anikin, V. S. Differalʹnye priblizhenii͡a︡ funkt͡s︡iĭ. Izd-vo "Fan" Uzbekskoĭ SSR, 1988.

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31

Németh, Géza. Mathematical approximation of special functions: Ten papers on Chebyshev expansions. Nova Science Publishers, 1992.

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32

Naisse, J. P. L' approximation analytique: Vers une théorie empirique constructive et finie. Editions de l'Université de Bruxelles, 1992.

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33

Mitrinović, D. S., J. E. Pečarić, and A. M. Fink. Inequalities Involving Functions and Their Integrals and Derivatives. Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-011-3562-7.

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34

E, Pečarić J., and Fink A. M. 1932-, eds. Inequalities involving functions and their integrals and derivatives. Kluwer Academic Publishers, 1991.

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35

Horing, Norman J. Morgenstern. Non-Equilibrium Green’s Functions: Variational Relations and Approximations for Particle Interactions. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0009.

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Chapter 09 Nonequilibrium Green’s functions (NEGF), including coupled-correlated (C) single- and multi-particle Green’s functions, are defined as averages weighted with the time-development operator U(t0+τ,t0). Linear conductivity is exhibited as a two-particle equilibrium Green’s function (Kubo-type formulation). Admitting particle sources (S:η,η+) and non-conservation of number, the non-equilibrium multi-particle Green’s functions are constructed with numbers of creation and annihilation operators that may differ, and they may be derived as variational derivatives with respect to sources η,η+ of a generating functional eW=TrU(t0+τ,t0)CS/TrU(t0+τ,t0)C. (In the non-interacting case this yields the n-particle Green’s function as a permanent/determinant of single-particle Green’s functions.) These variational relations yield a symmetric set of multi-particle Green’s function equations. Cumulants and the Linked Cluster Theorem are discussed and the Random Phase Approximation (RPA) is derived variationally. Schwinger’s variational differential formulation of perturbation theories for the Green’s function, self-energy, vertex operator, and also shielded potential perturbation theory, are reviewed. The Langreth Algebra arises from analytic continuation of integration of products of Green’s functions in imaginary time to the real-time axis with time-ordering along the integration contour in the complex time plane. An account of the Generalized Kadanoff-Baym Ansatz is presented.

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36

Approximation of functions. 2nd ed. Chelsea Pub. Co., 1986.

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37

Nürnberger, Günther. Approximation by Spline Functions. Springer, 2013.

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38

Approximation by Spline Functions. 1989.

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39

Mashreghi, Javad. Derivatives of Inner Functions. Springer, 2014.

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40

Prolla, Joao B. Approximation of Vector Valued Functions. Elsevier Science & Technology Books, 2011.

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41

Approximation of Continuously Differentiable Functions. Elsevier, 1986. http://dx.doi.org/10.1016/s0304-0208(08)x7079-3.

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42

Petrushev, P. P., and Vasil Atanasov Popov. Rational Approximation of Real Functions. Cambridge University Press, 1988.

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43

Approximation of continuously differentiable functions. North-Holland, 1986.

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44

P, Singh S. Approximation Theory and Spline Functions. Springer, 2011.

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45

Petrushev, P. P., and Vasil Atanasov Popov. Rational Approximation of Real Functions. Cambridge University Press, 2013.

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46

Llavona, J. G. Approximation of Continuously Differentiable Functions. Elsevier Science & Technology Books, 1986.

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47

Petrushev, P. P., and Vasil Atanasov Popov. Rational Approximation of Real Functions. University of Cambridge ESOL Examinations, 2011.

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48

Burry, J. H. W., B. Watson, and Singh S. P. Approximation Theory and Spline Functions. Springer, 2012.

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49

Approximation Theory and Spline Functions. Springer, 2011.

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50

Fox, Raymond. The Use of Self. Oxford University Press, 2011. http://dx.doi.org/10.1093/oso/9780190616144.001.0001.

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This monograph presents recent advances in neural network (NN) approaches and applications to chemical reaction dynamics. Topics covered include: (i) the development of ab initio potential-energy surfaces (PES) for complex multichannel systems using modified novelty sampling and feedforward NNs; (ii) methods for sampling the configuration space of critical importance, such as trajectory and novelty sampling methods and gradient fitting methods; (iii) parametrization of interatomic potential functions using a genetic algorithm accelerated with a NN; (iv) parametrization of analytic interatomic potential functions using NNs; (v) self-starting methods for obtaining analytic PES from ab inito electronic structure calculations using direct dynamics; (vi) development of a novel method, namely, combined function derivative approximation (CFDA) for simultaneous fitting of a PES and its corresponding force fields using feedforward neural networks; (vii) development of generalized PES using many-body expansions, NNs, and moiety energy approximations; (viii) NN methods for data analysis, reaction probabilities, and statistical error reduction in chemical reaction dynamics; (ix) accurate prediction of higher-level electronic structure energies (e.g. MP4 or higher) for large databases using NNs, lower-level (Hartree-Fock) energies, and small subsets of the higher-energy database; and finally (x) illustrative examples of NN applications to chemical reaction dynamics of increasing complexity starting from simple near equilibrium structures (vibrational state studies) to more complex non-adiabatic reactions. The monograph is prepared by an interdisciplinary group of researchers working as a team for nearly two decades at Oklahoma State University, Stillwater, OK with expertise in gas phase reaction dynamics; neural networks; various aspects of MD and Monte Carlo (MC) simulations of nanometric cutting, tribology, and material properties at nanoscale; scaling laws from atomistic to continuum; and neural networks applications to chemical reaction dynamics. It is anticipated that this emerging field of NN in chemical reaction dynamics will play an increasingly important role in MD, MC, and quantum mechanical studies in the years to come.

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