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51 
On the asymptotic behavior of the optimal error of spline interpolation of multivariate functionsBabenko, Yuliya. January 2006 (has links)
Thesis (Ph. D. in Mathematics)Vanderbilt University, Aug. 2006. / Title from title screen. Includes bibliographical references.

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Numerical solution of linear second order parabolic partial differential equations by the methods of collacation with cubic splinesDoedel, Eusebius Jacobus January 1973 (has links)
Collocation with cubic splines is used as a method for solving Linear second order parabolic partial differential equations. The collocation method is shown to be equivalent to a finite difference method that is consistent with the differential equation and stable in the sense of Von Neumann. Results of numerical computations are given, as well as an application of the method to a moving boundary problem for the heat equation. / Science, Faculty of / Mathematics, Department of / Graduate

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Sksplines de funções periódicas / Sksplines of periodic functionsLopes, Raquel Vieira, 1983 22 August 2018 (has links)
Orientador: Sérgio Antonio Tozoni / Dissertação (mestrado)  Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 20180822T06:19:51Z (GMT). No. of bitstreams: 1
Lopes_RaquelVieira_M.pdf: 1141005 bytes, checksum: 8091e673668abab031630ae7fd1b7436 (MD5)
Previous issue date: 2013 / Resumo: Os sksplines são uma generalização natural dos splines polinomiais, os quais foram introduzidos e tiveram sua teoria básica desenvolvida por Alexander Kushpel nos anos de 19831985. Estas funções são importantes em várias aplicações e seu espaço é gerado por translações discretas de uma única função núcleo. Neste trabalho, estudamos condições necessárias e suficientes para a existência e unicidade de sksplines interpolantes de funções periódicas. Além disso, estudamos a aproximação de funções de determinadas classes por sksplines nos espaços Lp. Como aplicação estudamos a aproximação de funções infinitamente diferenciáveis e finitamente diferenciáveis por sk splines / Abstract: The sksplines are a natural generalization of polynomial splines. They were introduced and their basic theory developed by Alexander Kushpel between 1983 and 1985. These functions are important in many applications and the space of sksplines is the linear span of shifts of a single kernel K. In this work, we study necessary and sufficient conditions for the existence and uniqueness of sksplines interpolants of periodic functions. Furthermore, we study the approximation in several classes of functions by sksplines in the Lp spaces. As an application we study the approximation of infinitely and finitely differentiable functions by sksplines / Mestrado / Matematica Aplicada / Mestra em Matemática Aplicada

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A duality approach to spline approximationBonawitz, Elizabeth Ann 02 March 2006 (has links)
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. / Ph. D.

55 
Computation of complex cepstrum.Bhanu, Bir January 1978 (has links)
Thesis. 1978. Elec.E.Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Includes bibliographical references. / Elec.E.

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Semiparametric latent variable models with Bayesian psplines. / CUHK electronic theses & dissertations collectionJanuary 2010 (has links)
In medical, behavioral, and socialpsychological sciences, latent variable models are useful in handling variables that cannot be directly measured by a single observed variable, but instead are assessed through a number of observed variables. Traditional latent variable models are usually based on parametric assumptions on both relations between outcome and explanatory latent variables, and error distributions. In this thesis, semiparametric models with Bayesian Psplines are developed to relax these rigid assumptions. / In the fourth part of the thesis, the methodology developed in the third part is further extended to a varying coefficient model with latent variables. Varying coefficient model is a class of flexible semiparametric models in which the effects of covariates are modeled dynamically by unspecified smooth functions. A transformation varying coefficient model can handle arbitrarily distributed dynamic data. A simulation study shows that our proposed method performs well in the analysis of this complex model. / In the last part of the thesis, we propose a finite mixture of varying coefficient models to analyze dynamic data with heterogeneity. A simulation study demonstrates that our proposed method can explore possible existence of different groups in a dynamic data, where in each group the dynamic influences of covariates on the response variables have different patterns. The proposed method is applied to a longitudinal study concerning the effectiveness of heroin treatment. Distinct patterns of heroin use and treatment effect in different patient groups are identified. / In the second part of the thesis, a latent variable model is proposed to relax the first assumption, in which unknown additive functions of latent variables in the structural equation are modeled by Bayesian Psplines. The estimation of nonparametric functions is based on powerful Markov chain Monte Carlo (MCMC) algorithm with block update scheme. A simulation study shows that the proposed method can handle much wider situation than traditional models. The proposed semiparametric latent variable model is applied to a study on osteoporosis prevention and control. Some interesting functional relations, which may be overlooked by traditional parametric latent variable models, are revealed. / In the third part of the thesis, a transformation model is developed to relax the second assumption, which usually assumes the normality of observed variables and random errors. In our proposed model, the nonnormal response variables are transformed to normal by unknown functions modeled with Bayesian Psplines. This semiparametric transformation model is shown to be applicable to a wide range of statistical analysis. The model is applied to a study on the intervention treatment of polydrug use in which the traditional model assumption is violated because many observed variables exhibit serious departure from normality. / Lu, Zhaohua. / Adviser: XinYuan Song. / Source: Dissertation Abstracts International, Volume: 7204, Section: B, page: . / Thesis (Ph.D.)Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 119130). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

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Variational and spline based multimodal nonrigid medical image registration and applications. / CUHK electronic theses & dissertations collectionJanuary 2005 (has links)
In the brain mapping case, the geodesic closest points are used as the anatomical constraints for the intersubject nonrigid registration. The method uses the anatomical constraint in the nonrigid registration which is much more reasonable for the anatomical correspondence. The registration result shows significant improvement comparing with the iterative closest points based method. / In the third application, we use the nonrigid registration method to register the different sweeps of freehand ultrasound images. We setup a 3D freehand ultrasound imaging system to capture images of a human anatomy such as liver, prostate, brain tumor and fetus. The arbitrary scanned image slices are reconstructed and resliced into volumetric dataset. We use a Bspline based nonrigid registration method to compounding different freehand ultrasound sweeps. This technique can be used to make 3D ultrasound models of fetus and other organs. / Medical image registration is an active research area during the last two decades. The registration technique can be widely used in the applications of the computer aided surgery, brain mapping and pathological detection and analysis. With the development of the computing power, fast and accurate registration techniques have been developed into necessary tools for quantitative analysis of the medical image. / Nonrigid registration methods can be used in atlas based image segmentation, intersubject brain image registration and 3D freehand ultrasound modeling. In one of our proposed novel segmentation methods, we interleave the segmentation and the registration processes by using the segmentation to provide the anatomical constraints for registration to improve the atlas based nonrigid registration. This updated registration can be used to improve the new segmentation. This process is repeated until a good result in segmentation is obtained. / The registration methods can be classified into rigid and nonrigid registrations according to whether the anatomy is locally deformed or not. According to the sensor by which the images are taken, the registration will be divided into monomodal and multimodal image registration. Since the invention of the medical imaging devices, great diversity of medical imaging sensors have been developed with different physical principles. In practice we have to face the problem of multimodal registration. In medical image analysis, we often have to consider the images of the human anatomy with deformable characteristics. In order to achieve this goal we need to use the voxel based registration method which considers all of the voxel information of the images in matching. There are several nonrigid registration approaches. However, the variational approach of nonrigid registration can represent the registration problem into a wellposed problem with a wellfounded mathematical base. In our work, we considered the forward and backward deformation functions and proposed a variational approach for a new consistent multimodal nonrigid registration method. By this way, we will find the forward and backward transform to be close to the inverse of each other. This makes the correspondence between two images more consistent and accurate. We use both explicit and implicit difference method to solve the EulerLagrange equation and the results show significant improvements in the transformation inverse consistency. Although variational approach for multimodal nonrigid registration can solve the nonrigid registration problem well, generally speaking, it is slow. The displacement of each voxel has to be calculated and the iteration time is very long since the number of the unknowns are large. Although a multiresolution strategy can be used to speed up, the registration problem is still slow when registering large medical datasets. The 3D Bspline based method has been used as an efficient method to register medical images since only a small number of control points are used to manipulate the local deformation field. In our work, we developed a 3D Bspline based consistent multimodal nonrigid registration method with an explicit representation of derivatives. The conventional optimization methods can be used to find the optimal parameters. We use a hierarchical Bspline refinement method to approximate the deformation function from larger to smaller scale. Since the derivatives of the cost function is represented in an explicit way, the computing is reduced. It is more efficient than directly computing the derivative of the cost function by using a numerical evaluation method. The method can be considered as a multigrid method for solving the consistent variational registration problem. The computing speed is increased by several times. The Bspline based method needs far less iterations to converge as its number of unknowns is small. / Zhang Zhijun. / "October 2005." / Source: Dissertation Abstracts International, Volume: 6711, Section: B, page: 6645. / Thesis (Ph.D.)Chinese University of Hong Kong, 2005. / Includes bibliographical references (p. 209233). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

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Adaptive knot location for spline approximation.Mier Muth, Alberto Mauricio January 1976 (has links)
Thesis. 1976. M.S.Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. / Microfiche copy available in Archives and Engineering. / Includes bibliographical references. / M.S.

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Statistical methods for function estimation and classificationKim, Heeyoung 20 June 2011 (has links)
This thesis consists of three chapters. The first chapter focuses on adaptive smoothing splines for fitting functions with varying roughness. In the first part of the first chapter, we study an asymptotically optimal procedure to choose the value of a discretized version of the variable smoothing parameter in adaptive smoothing splines. With the choice given by the multivariate version of the generalized cross validation, the resulting adaptive smoothing spline estimator is shown to be consistent and asymptotically optimal under some general conditions. In the second part, we derive the asymptotically optimal local penalty function, which is subsequently used for the derivation of the locally optimal smoothing spline estimator. In the second chapter, we propose a Lipschitz regularity based statistical model, and apply it to coordinate measuring machine (CMM) data to estimate the form error of a manufactured product and to determine the optimal sampling positions of CMM measurements. Our proposed waveletbased model takes advantage of the fact that the Lipschitz regularity holds for the CMM data. The third chapter focuses on the classification of functional data which are known to be well separable within a particular interval. We propose an interval based classifier. We first estimate a baseline of each class via convex optimization, and then identify an optimal interval that maximizes the difference among the baselines. Our interval based classifier is constructed based on the identified optimal interval. The derived classifier can be implemented via a loworderofcomplexity algorithm.

60 
Semiparametric regression with random effects /Lee, Sungwook, January 1997 (has links)
Thesis (Ph. D.)University of MissouriColumbia, 1997. / Typescript. Vita. Includes bibliographical references (leaves 114117). Also available on the Internet.

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