Books on the topic 'Approximations and expansions – Approximations and expansions – Padé; approximation'

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1

1968-, Arvesú Jorge, and Lopez Lagomasino Guillermo 1948-, eds. Recent advances in orthogonal polynomials, special functions, and their applications: 11th International Symposium on Orthogonal Polynomials, Special Functions, and Their Applications, August 29-September 2, 2011, Universidad Carlos III de Madrid, Leganes, Spain. Providence, R.I: American Mathematical Society, 2012.

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2

Jensen, J. L. Saddlepoint approximations, Edgeworth expansions and normal approximations: From independence to dependence. Aarhus C, Denmark: Dept. of Theoretical Statistics, Institute of Mathematics, University of Aarhus, 1993.

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3

Wong, R. Asymptotic approximations of integrals. Boston: Academic Press, 1989.

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4

Wong, R. Asymptotic approximations of integrals. Philadelphia: Society for Industrial and Applied Mathematics, 2001.

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5

service), SpringerLink (Online, ed. Algebraic Approximation: A Guide to Past and Current Solutions. Basel: Springer Basel AG, 2012.

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6

Pardalos, P. M. Nonlinear Analysis: Stability, Approximation, and Inequalities. New York, NY: Springer New York, 2012.

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7

1939-, Schumaker Larry L., and SpringerLink (Online service), eds. Approximation Theory XIII: San Antonio 2010. New York, NY: Springer Science+Business Media, LLC, 2012.

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8

Dai, Feng. Approximation Theory and Harmonic Analysis on Spheres and Balls. New York, NY: Springer New York, 2013.

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9

1962-, Petras Knut, ed. Quadrature theory: The theory of numerical integration on a compact interval. Providence, R.I: American Mathematical Society, 2011.

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10

Ervedoza, Sylvain. Numerical Approximation of Exact Controls for Waves. New York, NY: Springer New York, 2013.

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11

service), SpringerLink (Online, ed. Mathematics of Approximation. Paris: Atlantis Press, 2012.

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12

Michel, Volker. Lectures on Constructive Approximation: Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball. Boston: Birkhäuser Boston, 2013.

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13

Saff, E. B., Douglas Patten Hardin, Brian Z. Simanek, and D. S. Lubinsky. Modern trends in constructive function theory: Conference in honor of Ed Saff's 70th birthday : constructive functions 2014, May 26-30, 2014, Vanderbilt University, Nashville, Tennessee. Providence, Rhode Island: American Mathematical Society, 2016.

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14

Allen, Zalcman Lawrence, ed. Complex proofs of real theorems. Providence, R.I: American Mathematical Society, 2012.

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15

Schumaker, Larry, and Marian Neamtu. Approximation Theory XIII : San Antonio 2010: San Antonio 2010. Springer, 2014.

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16

Zuazua, Enrique, and Sylvain Ervedoza. Numerical Approximation of Exact Controls for Waves. Springer, 2013.

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17

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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18

Raff, Lionel, Ranga Komanduri, Martin Hagan, and Satish Bukkapatnam. Neural Networks in Chemical Reaction Dynamics. Oxford University Press, 2012. http://dx.doi.org/10.1093/oso/9780199765652.001.0001.

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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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