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Dissertations / Theses on the topic 'Approximation of derivatives of functions'

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Published: 5 June 2025

Last updated: 2 August 2025

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1

Deterding, Stephen. "Bounded Point Derivations on Certain Function Spaces." UKnowledge, 2018. https://uknowledge.uky.edu/math_etds/51.

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Let 𝑋 be a compact subset of the complex plane and denote by 𝑅𝑝(𝑋) the closure of rational functions with poles off 𝑋 in the 𝐿𝑝(𝑋) norm. We show that if a point 𝑥0 admits a bounded point derivation on 𝑅𝑝(𝑋) for 𝑝 > 2, then there is an approximate derivative at 𝑥0. We also prove a similar result for higher order bounded point derivations. This extends a result of Wang, which was proven for 𝑅(𝑋), the uniform closure of rational functions with poles off 𝑋. In addition, we show that if a point 𝑥0 admits a bounded point derivation on 𝑅(𝑋) and if 𝑋 contains an interior cone, then the bounded point d

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2

Al-Mohy, Awad. "Algorithms for the matrix exponential and its Fréchet derivative." Thesis, University of Manchester, 2011. https://www.research.manchester.ac.uk/portal/en/theses/algorithms-for-the-matrix-exponential-and-its-frechet-derivative(4de9bdbd-6d79-4e43-814a-197668694b8e).html.

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New algorithms for the matrix exponential and its Fréchet derivative are presented. First, we derive a new scaling and squaring algorithm (denoted expm[new]) for computing eA, where A is any square matrix, that mitigates the overscaling problem. The algorithm is built on the algorithm of Higham [SIAM J.Matrix Anal. Appl., 26(4): 1179-1193, 2005] but improves on it by two key features. The first, specific to triangular matrices, is to compute the diagonal elements in the squaring phase as exponentials instead of powering them. The second is to base the backward error analysis that underlies the

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3

Yang, Qianqian. "Novel analytical and numerical methods for solving fractional dynamical systems." Thesis, Queensland University of Technology, 2010. https://eprints.qut.edu.au/35750/1/Qianqian_Yang_Thesis.pdf.

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During the past three decades, the subject of fractional calculus (that is, calculus of integrals and derivatives of arbitrary order) has gained considerable popularity and importance, mainly due to its demonstrated applications in numerous diverse and widespread fields in science and engineering. For example, fractional calculus has been successfully applied to problems in system biology, physics, chemistry and biochemistry, hydrology, medicine, and finance. In many cases these new fractional-order models are more adequate than the previously used integer-order models, because fractional deri

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4

Kárský, Vilém. "Modelování LTI SISO systémů zlomkového řádu s využitím zobecněných Laguerrových funkcí." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2017. http://www.nusl.cz/ntk/nusl-316278.

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This paper concentrates on the description of fractional order LTI SISO systems using generalized Laguerre functions. There are properties of generalized Laguerre functions described in the paper, and an orthogonal base of these functions is shown. Next the concept of fractional derivatives is explained. The last part of this paper deals with the representation of fractional order LTI SISO systems using generalized Laguerre functions. Several examples were solved to demonstrate the benefits of using these functions for the representation of LTI SISO systems.

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5

Ugolotti, Alessandro. "Alternative derivative expansion in Functional RG and application." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amslaurea.unibo.it/10434/.

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We give a brief review of the Functional Renormalization method in quantum field theory, which is intrinsically non perturbative, in terms of both the Polchinski equation for the Wilsonian action and the Wetterich equation for the generator of the proper verteces. For the latter case we show a simple application for a theory with one real scalar field within the LPA and LPA' approximations. For the first case, instead, we give a covariant "Hamiltonian" version of the Polchinski equation which consists in doing a Legendre transform of the flow for the corresponding effective Lagrangian replac

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6

Martin, David Royce. "Quadrature Approximation of Matrix Functions, with Applications." Kent State University / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=kent1337658656.

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7

Hed, Lisa. "Approximation and Subextension of Negative Plurisubharmonic Functions." Licentiate thesis, Umeå : Department of Mathematics and Mathematical Statistics, Umeå University, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-1799.

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8

Zhu, Shengxin. "Numerical linear approximation involving radial basis functions." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:b870646b-5155-45f8-b38c-ae6cf4d22f27.

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This thesis aims to acquire, deepen and promote understanding of computing techniques for high dimensional scattered data approximation with radial basis functions. The main contributions of this thesis include sufficient conditions for the sovability of compactly supported radial basis functions with different shapes, near points preconditioning techniques for high dimensional interpolation systems with compactly supported radial basis functions, a heterogeneous hierarchical radial basis function interpolation scheme, which allows compactly supported radial basis functions of different shapes

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9

Beaty, Michael Graeme. "Reconstructing functions from values and derivatives." Thesis, University of York, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.329630.

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10

Liu, Shenhui. "Automorphic L-Functions and Their Derivatives." The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1499965951825371.

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11

Hermanns, Sebastian [Verfasser]. "Nonequilibrium Green functions - selfenergy approximation techniques / Sebastian Hermanns." Kiel : Universitätsbibliothek Kiel, 2017. http://d-nb.info/1143595246/34.

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12

Schreiner, Michael [Verfasser]. "Wavelet Approximation by Spherical Up Functions / Michael Schreiner." Aachen : Shaker, 2004. http://d-nb.info/1170537413/34.

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13

McQuillan, Colin. "The computational complexity of approximation of partition functions." Thesis, University of Liverpool, 2013. http://livrepository.liverpool.ac.uk/12893/.

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This thesis studies the computational complexity of approximately evaluating partition functions. For various classes of partition functions, we investigate whether there is an FPRAS: a fully polynomial randomised approximation scheme. In many of these settings we also study 'expressibility', a simple notion of defining a constraint by combining other constraints, and we show that the results cannot be extended by expressibility reductions alone. The main contributions are: • We show that there is no FPRAS for evaluating the partition function of the hard-core gas model on planar graphs at fug

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14

Valenzuela, Zaldy M. "Constant and power-of-2 segmentation algorithms for a high speed numerical function generator." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 2005. http://library.nps.navy.mil/uhtbin/hyperion/05Jun%5FValenzuela.pdf.

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15

Li, Deyuan. "On extreme value approximation to tails of distribution functions." [Amsterdam : Rotterdam : Thela Thesis] ; Erasmus University [Host], 2004. http://hdl.handle.net/1765/6778.

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16

Rovinsky, Marat. "Multiple gamma functions and derivatives of L-functions at non-positive integers." Thesis, Massachusetts Institute of Technology, 1996. http://hdl.handle.net/1721.1/38407.

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17

Johnson, William Joel Dietmar. "Rational fraction approximations for passive network functions." [Tampa, Fla.] : University of South Florida, 2005. http://purl.fcla.edu/fcla/etd/SFE0001083.

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18

Nicks, Daniel A. "Value distribution of meromorphic functions and their derivatives." Thesis, University of Nottingham, 2010. http://eprints.nottingham.ac.uk/11327/.

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The content of this thesis can be divided into two broad topics. The first half investigates the deficient values and deficient functions of certain classes of meromorphic functions. Here a value is called deficient if a function takes that value less often than it takes most other values. It is shown that the derivative of a periodic meromorphic function has no finite non-zero deficient values, provided that the function satisfies a necessary growth condition. The classes B and S consist of those meromorphic functions for which the finite critical and asymptotic values form a bounded or finit

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19

Zhang, Kai. "Kernel-based clustering and low rank approximation /." View abstract or full-text, 2008. http://library.ust.hk/cgi/db/thesis.pl?CSED%202008%20ZHANG.

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20

Soler, i. Gibert Odí. "Approximation in the Zygmund Class and Distortion under Inner Functions." Doctoral thesis, Universitat Autònoma de Barcelona, 2020. http://hdl.handle.net/10803/670865.

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En aquest treball es tracten dos problemes. El primer és un problema d’aproximació en la classe de Zygmund per funcions del subespai I_1(BMO), que és l’espai de funcions contínues amb derivada a BMO en el sentit de les distribucions. Considerem la distància definida per la semi-norma de Zygmund. En el Capítol 1, donada una funció f de la classe de Zygmund en la recta real amb suport compacte, trobem una estimació de la seva distància al subespai I_1(BMO). A més, aquest resultat s’expressa en termes de les segones diferències de f, que defineixen la seva semi-norma de Zygmund. Com a corol·lari,

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21

Shabbir, Muhammad [Verfasser]. "Approximation of chirp functions by fractional Fourier series / Muhammad Shabbir." Lübeck : Zentrale Hochschulbibliothek Lübeck, 2019. http://d-nb.info/1194435505/34.

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22

Falco, Benavent Francisco Javier. "Complex approximation and fibers of Banach algebras of analytic functions." Kent State University / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=kent1478016863252231.

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23

Sánchez, Álvarez José Manuel. "Semi-lipschitz functions, best approximation, and fuzzy quasi-metric hyperspaces." Doctoral thesis, Universitat Politècnica de València, 2009. http://hdl.handle.net/10251/5769.

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En los últimos años se ha desarrollado una teoría matemática que permite generalizar algunas teorías matemáticas clásicas: hiperespacios, espacios de funciones, topología algebraica, etc. Este hecho viene motivado, en parte, por ciertos problemas de análisis funcional, concentración de medidas, sistemas dinámicos, teoría de las ciencias de la computación, matemática económica, etc. Esta tesis doctoral está dedicada al estudio de algunas de estas generalizaciones desde un punto de vista no simétrico. En la primera parte, estudiamos el conjunto de funciones semi-Lipschitz; mostramos que este

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24

Bonawitz, Elizabeth Ann. "A duality approach to spline approximation." Diss., Virginia Tech, 1994. http://hdl.handle.net/10919/37448.

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This dissertation discusses a new approach to spline approximation. A periodic spline approximation 𝑓<sub>M,m,N</sub>(x) = Σ<sub>k=1</sub><sup>N</sup>α<sub>k</sub>Φ<sub>M,k</sub>(x) to a periodic function 𝑓(x) is determined by requiring < Φ<sub>m,j</sub>, 𝑓 - 𝑓<sub>M,m,N</sub> > = 0 for j = 1,...,N, where the Φ<sub>L,k</sub>'s are the unique periodic spline basis functions of order 𝐿. Error estimates, examples and some relationships to wavelets are given for the case M - m = 2μ. The case M - m = 2µ + 1 is briefly discussed but not completely explored.<br>Ph. D.

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25

Dawson, Dan Paul. "Concerning Integral Approximations of Bounded Finitely Additive Set Functions." Thesis, University of North Texas, 1992. https://digital.library.unt.edu/ark:/67531/metadc332650/.

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The purpose of this paper is to generalize a theorem that characterizes absolute continuity of bounded finitely additive set functions in the form of an integral approximation. We show that his integral exists if the condition of absolute continuity is removed.

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26

Ghosh, Bimalendu. "Generalized continuous functions, derivatives and integrals of perron type." Thesis, University of North Bengal, 1990. http://hdl.handle.net/123456789/606.

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27

Lowitzsch, Svenja. "Approximation and interpolation employing divergence-free radial basis functions with applications." Texas A&M University, 2003. http://hdl.handle.net/1969.1/21.

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Approximation and interpolation employing radial basis functions has found important applications since the early 1980's in areas such as signal processing, medical imaging, as well as neural networks. Several applications demand that certain physical properties be fulfilled, such as a function being divergence free. No such class of radial basis functions that reflects these physical properties was known until 1994, when Narcowich and Ward introduced a family of matrix-valued radial basis functions that are divergence free. They also obtained error bounds and stability estimates fo

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28

Munir, A. U. K. "Series representations and approximation of some quantile functions appearing in finance." Thesis, University College London (University of London), 2013. http://discovery.ucl.ac.uk/1383796/.

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It has long been agreed by academics that the inversion method is the method of choice for generating random variates, given the availability of a cheap but accurate approximation of the quantile function. However for several probability distributions arising in practice a satisfactory method of approximating these functions is not available. The main focus of this thesis will be to develop Taylor and asymptotic series representations for quantile functions of the following probability distributions; Variance Gamma, Generalized Inverse Gaussian, Hyperbolic, -Stable and Snedecor’s F distributio

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29

Hertz, Erik. "Methodologies for Approximation of Unary Functions and Their Implementation in Hardware." Doctoral thesis, Högskolan i Halmstad, Centrum för forskning om inbyggda system (CERES), 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:hh:diva-30983.

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Applications in computer graphics, digital signal processing, communication systems, robotics, astrophysics, fluid physics and many other areas have evolved to become very computation intensive. Algorithms are becoming increasingly complex and require higher accuracy in the computations. In addition, software solutions for these applications are in many cases not sufficient in terms of performance. A hardware implementation is therefore needed. A recurring bottleneck in the algorithms is the performance of the approximations of unary functions, such as trigonometric functions, logarithms and t

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30

Le, Gia Quoc Thong. "Approximation of linear partial differential equations on spheres." Texas A&M University, 2003. http://hdl.handle.net/1969.1/22.

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The theory of interpolation and approximation of solutions to differential and integral equations on spheres has attracted considerable interest in recent years; it has also been applied fruitfully in fields such as physical geodesy, potential theory, oceanography, and meteorology. In this dissertation we study the approximation of linear partial differential equations on spheres, namely a class of elliptic partial differential equations and the heat equation on the unit sphere. The shifts of a spherical basis function are used to construct the approximate solution. In the elliptic case, both

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31

Jayakumar, Adithya. "Simulation-based optimization of Hybrid Systems Using Derivative Free Optimization Techniques." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1531954151797307.

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32

Weise, Michael. "A note on the second derivatives of rHCT basis functions." Universitätsbibliothek Chemnitz, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-154344.

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We consider reduced Hsieh-Clough-Tocher basis functions with respect to a splitting into subtriangles at the barycenter of the original triangular element. This article gives a proof that the second derivatives of those functions, which in general may jump at the subtriangle boundaries, do not jump at the barycenter.

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33

Richter, Christian. "Entropy and the approximation of functions on compact metric and topological spaces." [S.l.] : [s.n.], 2001. http://deposit.ddb.de/cgi-bin/dokserv?idn=963690264.

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34

Gorodetsky, Alex Arkady. "A learning method for the approximation of discontinuous functions for stochastic simulations." Thesis, Massachusetts Institute of Technology, 2012. http://hdl.handle.net/1721.1/76101.

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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2012.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (p. 79-83).<br>Surrogate models for computational simulations are inexpensive input-output approximations that allow expensive analyses, such as the forward propagation of uncertainty and Bayesian statistical inference, to be performed efficiently. When a simulation output does not depend smoothly on its inputs, however, most existing surrogate construction methodologies yield large errors and slow convergence rates.

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35

Relton, Samuel. "Algorithms for matrix functions and their Fréchet derivatives and condition numbers." Thesis, University of Manchester, 2015. https://www.research.manchester.ac.uk/portal/en/theses/algorithms-for-matrix-functions-and-their-frechet-derivatives-and-condition-numbers(f20e8144-1aa0-45fb-9411-ddc0dc7c2c31).html.

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36

Weise, Michael. "A note on the second derivatives of rHCT basis functions - extended." Universitätsbibliothek Chemnitz, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-160168.

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We consider reduced Hsieh-Clough-Tocher basis functions with respect to a splitting into subtriangles at an arbitrary interior point of the original triangular element. This article gives a proof that the second derivatives of those functions, which in general may jump at the subtriangle boundaries, do not jump at the splitting point.

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37

Eshghi, Nasim. "APPROXIMATION OF MATRIX FUNCTIONS BY QUADRATURE RULES BASED ON THELANCZOS OR ARNOLDI PROCESSES." Kent State University / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=kent1603537330615922.

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38

Haberstich, Cécile. "Adaptive approximation of high-dimensional functions with tree tensor networks for Uncertainty Quantification." Thesis, Ecole centrale de Nantes, 2020. http://www.theses.fr/2020ECDN0045.

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Les problèmes de quantification d'incertitudes des modèles numériques nécessitent de nombreuses simulations, souvent très coûteuses (en temps de calcul et/ou en mémoire). C'est pourquoi il est essentiel de construire des modèles approchés qui sont moins coûteux à évaluer. En pratique, si la réponse d'un modèle numérique est représentée par une fonction, on cherche à en construire une approximation.L'objectif de cette thèse est de construire l'approximation d'une fonction qui soit contrôlée tout en utilisant le moins d'évaluations possible de la fonction.Dans un premier temps, nous proposons un

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39

Nahapetyan, Artyom. "Nonlinear approximation techniques to solve network flow problems with nonlinear arc cost functions." [Gainesville, Fla.] : University of Florida, 2006. http://purl.fcla.edu/fcla/etd/UFE0015623.

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40

Lee, Jae S. (Jae Seung). "Continuous, Nowhere-Differentiable Functions with no Finite or Infinite One-Sided Derivative Anywhere." Thesis, University of North Texas, 1994. https://digital.library.unt.edu/ark:/67531/metadc278627/.

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In this paper, we study continuous functions with no finite or infinite one-sided derivative anywhere. In 1925, A. S. Beskovitch published an example of such a function. Since then we call them Beskovitch functions. This construction is presented in chapter 2, The example was simple enough to clear the doubts about the existence of Besicovitch functions. In 1932, S. Saks showed that the set of Besicovitch functions is only a meager set in C[0,1]. Thus the Baire category method for showing the existence of Besicovitch functions cannot be directly applied. A. P. Morse in 1938 constructed Besicov

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41

Farrell, Patricio. "Multilevel collocation with radial basis functions." Thesis, University of Oxford, 2014. https://ora.ox.ac.uk/objects/uuid:9fd99f0f-2556-41eb-8bcd-5b9256296a17.

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In this thesis, we analyse multilevel collocation methods involving compactly supported radial basis functions. We focus on linear second-order elliptic bound- ary value problems as well as Darcy's problem. While in the former case we use scalar-valued positive definite functions for constructing multilevel approximants, in the latter case we use matrix-valued functions that are automatically divergence-free. A similar result is presented for interpolating divergence-free vector fields. Even though it had been observed more than a decade ago that the stationary setting, i.e. when the support r

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42

Heimonen, A. (Ari). "On effective irrationality measures for some values of certain hypergeometric functions." Doctoral thesis, University of Oulu, 1997. http://urn.fi/urn:isbn:9514247191.

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Abstract The dissertation consists of three articles in which irrationality measures for some values of certain special cases of the Gauss hypergeometric function are considered in both archimedean and non-archimedean metrics. The first presents a general result and a divisibility criterion for certain products of binomial coefficients upon which the sharpenings of the general result in special cases rely. The paper also provides an improvement concerning th e values of the logarithmic function. The second paper includes two other special cases, the first of which gives irrationality measures

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43

Morini, Massimiliano. "Free-discontinuity problems: calibration and approximation of solutions." Doctoral thesis, SISSA, 2001. http://hdl.handle.net/20.500.11767/3923.

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44

Javed, Mohsin. "Algorithms for trigonometric polynomial and rational approximation." Thesis, University of Oxford, 2016. https://ora.ox.ac.uk/objects/uuid:23a36d72-0299-4c63-98e8-d0aa088c062e.

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This thesis presents new numerical algorithms for approximating functions by trigonometric polynomials and trigonometric rational functions. We begin by reviewing trigonometric polynomial interpolation and the barycentric formula for trigonometric polynomial interpolation in Chapter 1. Another feature of this chapter is the use of the complex plane, contour integrals and phase portraits for visualising various properties and relationships between periodic functions and their Laurent and trigonometric series. We also derive a periodic analogue of the Hermite integral formula which enables us to

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45

GURUMURTHY, ARAVIND. "A GENETIC ALGORITHM TECHNIQUE FOR APPROXIMATING FUNCTIONS OF MULTIPLE INDEPENDENT VARIABLES." University of Cincinnati / OhioLINK, 2003. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1065654138.

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46

Hauser, James William. "Approximation of Nonlinear Functions for Fixed-Point and ASIC Applications Using a Genetic Algorithm." University of Cincinnati / OhioLINK, 2001. http://rave.ohiolink.edu/etdc/view?acc_num=ucin997989329.

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47

Iurlano, Flaviana. "An Approximation Result for Generalised Functions of Bounded Deformation and Applications to Damage Problems." Doctoral thesis, SISSA, 2013. http://hdl.handle.net/20.500.11767/4831.

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48

Ko, Hong Fu. "Marcinkiewicz's theorem and its generalizations /." View abstract or full-text, 2004. http://library.ust.hk/cgi/db/thesis.pl?MATH%202004%20KO.

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49

Pan, Minzhe. "Detection and approximation of function of two variables in high dimensions." Master's thesis, University of Central Florida, 2010. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/4556.

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This thesis originates from the deterministic algorithm of DeVore, Petrova, and Wojtaszcsyk for the detection and approximation of functions of one variable in high dimensions. We propose a deterministic algorithm for the detection and approximation of function of two variables in high dimensions.<br>ID: 029050403; System requirements: World Wide Web browser and PDF reader.; Mode of access: World Wide Web.; Thesis (M.S.)--University of Central Florida, 2010.; Includes bibliographical references (p. 49).<br>M.S.<br>Masters<br>Department of Mathematics<br>Sciences

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50

Feng, Limin. "JAMES-STEIN TYPE COMPOUND ESTIMATION OF MULTIPLE MEAN RESPONSE FUNCTIONS AND THEIR DERIVATIVES." UKnowledge, 2013. http://uknowledge.uky.edu/statistics_etds/6.

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Charnigo and Srinivasan originally developed compound estimators to nonparametrically estimate mean response functions and their derivatives simultaneously when there is one response variable and one covariate. The compound estimator maintains self consistency and almost optimal convergence rate. This dissertation studies, in part, compound estimation with multiple responses and/or covariates. An empirical comparison of compound estimation, local regression and spline smoothing is included, and near optimal convergence rates are established in the presence of multiple covariates. James and Ste

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