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Dissertations / Theses on the topic 'The Method of Least Squares'

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Published: 4 June 2021

Last updated: 1 February 2022

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1

Kong, Seunghyun. "Linear programming algorithms using least-squares method." Diss., Available online, Georgia Institute of Technology, 2007, 2007. http://etd.gatech.edu/theses/available/etd-04012007-010244/.

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Thesis (Ph. D.)--Industrial and Systems Engineering, Georgia Institute of Technology, 2007.<br>Martin Savelsbergh, Committee Member ; Joel Sokol, Committee Member ; Earl Barnes, Committee Co-Chair ; Ellis L. Johnson, Committee Chair ; Prasad Tetali, Committee Member.

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2

Huang, Xuejun, and Xuewen Huang. "The Least-Squares Method for American Option Pricing." Thesis, Uppsala University, Department of Mathematics, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-119754.

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3

Silva, Aristeguieta Maria. "Optimization of seismic least-squares inversion /." Access abstract and link to full text, 1993. http://0-wwwlib.umi.com.library.utulsa.edu/dissertations/fullcit/9325432.

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4

Kattelans, Thorsten. "The least squares spectral collocation method for incompressible flows." Berlin Köster, 2009. http://d-nb.info/997987812/04.

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5

Johnsen, Eivind. "Application method of the least squares finite element method to fracture mechanics." Thesis, Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/16435.

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6

Kolev, Tzanio Valentinov. "Least-squares methods for computational electromagnetics." Texas A&M University, 2004. http://hdl.handle.net/1969.1/1115.

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The modeling of electromagnetic phenomena described by the Maxwell's equations is of critical importance in many practical applications. The numerical simulation of these equations is challenging and much more involved than initially believed. Consequently, many discretization techniques, most of them quite complicated, have been proposed. In this dissertation, we present and analyze a new methodology for approximation of the time-harmonic Maxwell's equations. It is an extension of the negative-norm least-squares finite element approach which has been applied successfully to a variety of ot

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7

LIMA, CLEIDE MAYRA MENEZES. "A STUDY ABOUT THE ITERATED APPROXIMATED MOVING LEAST SQUARES METHOD." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2009. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=15003@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO<br>COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR<br>Esta dissertação tem por objetivo estudar um método para aproximação de dados esparços multivariados denominado o método Mínimos Quadrados Móveis por Aproximações Iteradas (Iterated Approximate Moving Least-Square Approximation – IAMLA). Este método é baseado no método de interpolação por funções de base radial (RBF) e no método de aproximação AMLS. Mas diferentemente do método RBF, ele não requer a solução de um sistema de equações lineares. O método IAMLS no limite converge p

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8

Bringmann, Philipp. "Adaptive least-squares finite element method with optimal convergence rates." Doctoral thesis, Humboldt-Universität zu Berlin, 2021. http://dx.doi.org/10.18452/22350.

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Die Least-Squares Finite-Elemente-Methoden (LSFEMn) basieren auf der Minimierung des Least-Squares-Funktionals, das aus quadrierten Normen der Residuen eines Systems von partiellen Differentialgleichungen erster Ordnung besteht. Dieses Funktional liefert einen a posteriori Fehlerschätzer und ermöglicht die adaptive Verfeinerung des zugrundeliegenden Netzes. Aus zwei Gründen versagen die gängigen Methoden zum Beweis optimaler Konvergenzraten, wie sie in Carstensen, Feischl, Page und Praetorius (Comp. Math. Appl., 67(6), 2014) zusammengefasst werden. Erstens scheinen fehlende Vorfaktoren proport

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9

Yano, Masayuki Ph D. Massachusetts Institute of Technology. "Massively parallel solver for the high-order Galerkin Least-Squares method." Thesis, Massachusetts Institute of Technology, 2009. http://hdl.handle.net/1721.1/54217.

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Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2009.<br>This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.<br>Cataloged from student submitted PDF version of thesis.<br>Includes bibliographical references (p. 85-91).<br>A high-order Galerkin Least-Squares (GLS) finite element discretization is combined with massively parallel implicit solvers. The stabilization parameter of the GLS discretization is modified to improve the resolution characteri

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10

Petra, Stefania. "Semismooth least squares methods for complementarity problems." Doctoral thesis, [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=98174558X.

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11

TORTURELA, ALEXANDRE DE MACEDO. "NOVEL SPARSE SYSTEMS LEAST SQUARES ESTIMATION METHODS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2014. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=26712@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO<br>INSTITUTO MILITAR DE ENGENHARIA<br>CENTRO TECNOLÓGICO DO EXÉRCITO<br>INSTITUTO DE PESQUISA E DESENVOLVIMENTO<br>Neste trabalho, quatro métodos projetados especificamente para a estimação de sistemas esparsos são originalmente elaborados e apresentados. São eles: Encolhimentos Sucessivos, Expansões Sucessivas, Minimização da Norma l1 e Ajuste Automático do fator de regularização do Custo LS. Os quatro métodos propostos baseiam-se na técnica de estimação de sistemas lineares e invariantes no tempo pelo critério dos mínimos quadrados, universa

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12

Guo, Ronggang. "Systematical analysis of the transformation procedures in Baden-Württemberg with Least Squares and Total Least Squares methods." Stuttgart : Universitätsbibliothek der Universität Stuttgart, 2007. http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-33293.

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13

Goktolga, Mustafa Ugur. "Simulation Of Conjugate Heat Transfer Problems Using Least Squares Finite Element Method." Master's thesis, METU, 2012. http://etd.lib.metu.edu.tr/upload/12614787/index.pdf.

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In this thesis study, a least-squares finite element method (LSFEM) based conjugate heat transfer solver was developed. In the mentioned solver, fluid flow and heat transfer computations were performed separately. This means that the calculated velocity values in the flow calculation part were exported to the heat transfer part to be used in the convective part of the energy equation. Incompressible Navier-Stokes equations were used in the flow simulations. In conjugate heat transfer computations, it is required to calculate the heat transfer in both flow field and solid region. In this study,

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14

Shan, Shidong. "A Levenberg-Marquardt method for large-scale bound-constrained nonlinear least-squares." Thesis, University of British Columbia, 2008. http://hdl.handle.net/2429/5648.

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The well known Levenberg-Marquardt method is used extensively for solving nonlinear least-squares problems. We describe an extension of the Levenberg- Marquardt method to problems with bound constraints on the variables. Each iteration of our algorithm approximately solves a linear least-squares problem subject to the original bound constraints. Our approach is especially suited to large-scale problems whose functions are expensive to compute; only matrix-vector products with the Jacobian are required. We present the results of numerical experiments that illustrate the effectiveness of the app

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15

Bringmann, Philipp [Verfasser]. "Adaptive least-squares finite element method with optimal convergence rates / Philipp Bringmann." Berlin : Humboldt-Universität zu Berlin, 2021. http://d-nb.info/1226153186/34.

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16

Prabhakar, Vivek. "Least squares based finite element formulations and their applications in fluid mechanics." [College Station, Tex. : Texas A&M University, 2006. http://hdl.handle.net/1969.1/ETD-TAMU-1152.

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17

Storn, Johannes. "Topics in Least-Squares and Discontinuous Petrov-Galerkin Finite Element Analysis." Doctoral thesis, Humboldt-Universität zu Berlin, 2019. http://dx.doi.org/10.18452/20141.

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Aufgrund der fundamentalen Bedeutung partieller Differentialgleichungen zur Beschreibung von Phänomenen in angewandten Wissenschaften ist deren Analyse ein Kerngebiet der Mathematik. Durch Computer lassen sich die Lösungen für eine Vielzahl dieser Gleichungen näherungsweise bestimmen. Die dabei verwendeten numerischen Verfahren sollen auf möglichst exakte Approximationen führen und deren Genauigkeit verifizieren. Die Least-Squares Finite-Elemente-Methode (LSFEM) und die unstetige Petrov-Galerkin (DPG) Methode sind solche Verfahren. Sie werden in dieser Dissertation untersucht. Der erste Tei

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18

Bochev, Pavel B. "Least squares finite element methods for the Stokes and Navier-Stokes equations." Diss., This resource online, 1994. http://scholar.lib.vt.edu/theses/available/etd-06062008-165910/.

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19

Darbeheshti, Neda. "Modification of the least-squares collocation method for non-stationary gravity field modelling." Curtin University of Technology, Department of Spatial Sciences, 2009. http://espace.library.curtin.edu.au:80/R/?func=dbin-jump-full&object_id=120241.

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Geodesy deals with the accurate analysis of spatial and temporal variations in the geometry and physics of the Earth at local and global scales. In geodesy, least-squares collocation (LSC) is a bridge between the physical and statistical understanding of different functionals of the gravitational field of the Earth. This thesis specifically focuses on the [incorrect] implicit LSC assumptions of isotropy and homogeneity that create limitations on the application of LSC in non-stationary gravity field modeling. In particular, the work seeks to derive expressions for local and global analytical c

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20

Cheng, Gang. "The nonparametric least-squares method for estimating monotone functions with interval-censored observations." Diss., University of Iowa, 2012. https://ir.uiowa.edu/etd/2839.

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Monotone function, such as growth function and cumulative distribution function, is often a study of interest in statistical literature. In this dissertation, we propose a nonparametric least-squares method for estimating monotone functions induced from stochastic processes in which the starting time of the process is subject to interval censoring. We apply this method to estimate the mean function of tumor growth with the data from either animal experiments or tumor screening programs to investigate tumor progression. In

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21

Li, Siqing. "Kernel-based least-squares approximations: theories and applications." HKBU Institutional Repository, 2018. https://repository.hkbu.edu.hk/etd_oa/539.

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Kernel-based meshless methods for approximating functions and solutions of partial differential equations have many applications in engineering fields. As only scattered data are used, meshless methods using radial basis functions can be extended to complicated geometry and high-dimensional problems. In this thesis, kernel-based least-squares methods will be used to solve several direct and inverse problems. In chapter 2, we consider discrete least-squares methods using radial basis functions. A general l^2-Tikhonov regularization with W_2^m-penalty is considered. We provide error estimates th

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22

Copeland, Dylan Matthew. "Negative-norm least-squares methods for axisymmetric Maxwell equations." Texas A&M University, 2006. http://hdl.handle.net/1969.1/3837.

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We develop negative-norm least-squares methods to solve the three-dimensional Maxwell equations for static and time-harmonic electromagnetic fields in the case of axial symmetry. The methods compute solutions in a two-dimensional cross section of the domain, thereby reducing the dimension of the problem from three to two. To achieve this dimension reduction, we work with weighted spaces in cylindrical coordinates. In this setting, approximation spaces consisting of low order finite element functions and bubble functions are analyzed. In contrast to other methods for axisymmetric Maxwell equati

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23

Yang, Xiaohua. "Numerical methods for box-constrained integer least squares problems." Thesis, McGill University, 2008. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=22038.

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Integer least squares (ILS) problems arise from many applications, such as communications, lattice design, and global navigation satellite systems. However, an ILS problem is NP-hard. The objective of this thesis is to design efficient algorithms for solving box-constrained overdetermined integer least squares (BOILS) problems and box-constrained underdetermined integer least squares (BUILS) problems. A typical method to solve ILS problems consists of two stages: reduction and search. For solving the BOILS problems, we propose a new reduction algorithm and a modified search algorithm. Unlike

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24

Galrinho, Miguel. "Least Squares Methods for System Identification of Structured Models." Licentiate thesis, KTH, Reglerteknik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-190947.

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The purpose of system identification is to build mathematical models for dynamical systems from experimental data. With the current increase in complexity of engineering systems, an important challenge is to develop accurate and computationally efficient algorithms. For estimation of parametric models, the prediction error method (PEM) is a benchmark in the field. When the noise is Gaussian and a quadratic cost function is used, PEM provides asymptotically efficient estimates if the model orders are correct. A disadvantage with PEM is that, in general, it requires minimizing a non-convex funct

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25

Kupferer, Stephan. "Anwendung der Total-Least-Squares-Technik bei geodätischen Problemstellungen." Karlsruhe : Univ.-Verl. Karlsruhe, 2005. http://deposit.d-nb.de/cgi-bin/dokserv?idn=97644576X.

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26

Kadapa, Chennakesava. "Mixed Galerkin and least-squares formulations for isogeometric analysis." Thesis, Swansea University, 2014. https://cronfa.swan.ac.uk/Record/cronfa42221.

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This work is concerned with the use of isogeometric analysis based on Non- Uniform Rational B-Splines (NURBS) to develop efficient and robust numerical techniques to deal with the problems of incompressibility in the fields of solid and fluid mechanics. Towards this, two types of formulations, mixed Galerkin and least-squares, are studied. During the first phase of this work, mixed Galerkin formulations, in the context of isogeometric analysis, are presented. Two-field and three-field mixed variational formulations - in both small and large strains - are presented to obtain accurate numerical

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27

Akdag, Osman. "Incompressible Flow Simulations Using Least Squares Spectral Element Method On Adaptively Refined Triangular Grids." Master's thesis, METU, 2012. http://etd.lib.metu.edu.tr/upload/12614944/index.pdf.

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The main purpose of this study is to develop a flow solver that employs triangular grids to solve two-dimensional, viscous, laminar, steady, incompressible flows. The flow solver is based on Least Squares Spectral Element Method (LSSEM). It has p-type adaptive mesh refinement/coarsening capability and supports p-type nonconforming element interfaces. To validate the developed flow solver several benchmark problems are studied and successful results are obtained. The performances of two different triangular nodal distributions, namely Lobatto distribution and Fekete distribution, are compared i

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28

Cheniae, Michael G. "Observability method for the least median of squares estimator as applied to power systems." Thesis, This resource online, 1991. http://scholar.lib.vt.edu/theses/available/etd-08142009-040309/.

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29

LIMA, URSULA SILVEIRA MONTEIRO DE. "COMPLEX DERIVATIVES VALUATION: APPLYING THE LEAST-SQUARES MONTE CARLO METHOD WITH SEVERAL POLYNOMIAL BASIS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2010. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=16812@1.

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CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO<br>Este trabalho tem por objetivo o estudo e a aplicação do Método de Mínimos Quadrados de Monte Carlo com diferentes bases polinomiais - Potência, Laguerre, Legendre e Hermite A - na precificação de Opções Asiáticas Americanas (Amerasian) tanto em sua modalidade de compra quanto em sua modalidade de venda. Os resultados encontrados ratificam a possibilidade de utilização alternativa de diversas bases polinomiais. Além disso, verifica-se a convergência em cada um dos experimentos, sem perder de vista a possibilidade de que haja, par

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30

Kochersberger, Kevin B. "A method of determining modal residues using an improved residual model and least squares." Diss., Virginia Tech, 1994. http://hdl.handle.net/10919/40166.

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A new approach to determining mode vectors is presented which uses predetermined global parameters and an improved residual model to iteratively determine modal residues. The motivation for such a technique is to determine modal parameters rapidly so that, as data acquisition techniques become faster, more structural degrees of freedom can be measured without significantly slowing down the parameter estimation process. The technique requires an accurate determination of the global parameters of natural frequency and damping by means of an FRF curve fit. More than one structural point is rec

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31

Moller, Jurgen Johann. "The implementation of noise addition partial least squares." Thesis, Stellenbosch : University of Stellenbosch, 2009. http://hdl.handle.net/10019.1/3362.

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Thesis (MComm (Statistics and Actuarial Science))--University of Stellenbosch, 2009.<br>When determining the chemical composition of a specimen, traditional laboratory techniques are often both expensive and time consuming. It is therefore preferable to employ more cost effective spectroscopic techniques such as near infrared (NIR). Traditionally, the calibration problem has been solved by means of multiple linear regression to specify the model between X and Y. Traditional regression techniques, however, quickly fail when using spectroscopic data, as the number of wavelengths can easily be se

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Cheng, Chao-heh. "Calculations for positioning with the Global Navigation Satellite System." Ohio : Ohio University, 1998. http://www.ohiolink.edu/etd/view.cgi?ohiou1176839268.

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33

Kim, Jingu. "Nonnegative matrix and tensor factorizations, least squares problems, and applications." Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/42909.

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Nonnegative matrix factorization (NMF) is a useful dimension reduction method that has been investigated and applied in various areas. NMF is considered for high-dimensional data in which each element has a nonnegative value, and it provides a low-rank approximation formed by factors whose elements are also nonnegative. The nonnegativity constraints imposed on the low-rank factors not only enable natural interpretation but also reveal the hidden structure of data. Extending the benefits of NMF to multidimensional arrays, nonnegative tensor factorization (NTF) has been shown to be successful in

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34

Wei, Fei. "Weighted least-squares finite element methods for PIV data assimilation." Thesis, Montana State University, 2011. http://etd.lib.montana.edu/etd/2011/wei/WeiF0811.pdf.

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The ability to diagnose irregular flow patterns clinically in the left ventricle (LV) is currently very challenging. One potential approach for non-invasively measuring blood flow dynamics in the LV is particle image velocimetry (PIV) using microbubbles. To obtain local flow velocity vectors and velocity maps, PIV software calculates displacements of microbubbles over a given time interval, which is typically determined by the actual frame rate. In addition to the PIV, ultrasound images of the left ventricle can be used to determine the wall position as a function of time, and the inflow and o

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35

Leary, Stephen J. "Least-Squares methods with adjustable nodes for steady hyperbolic PDEs." Thesis, University of Reading, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.312565.

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36

Akargun, Yigit Hayri. "Least-squares Finite Element Solution Of Euler Equations With Adaptive Mesh Refinement." Master's thesis, METU, 2012. http://etd.lib.metu.edu.tr/upload/12614138/index.pdf.

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Least-squares finite element method (LSFEM) is employed to simulate 2-D and axisymmetric flows governed by the compressible Euler equations. Least-squares formulation brings many advantages over classical Galerkin finite element methods. For non-self-adjoint systems, LSFEM result in symmetric positive-definite matrices which can be solved efficiently by iterative methods. Additionally, with a unified formulation it can work in all flight regimes from subsonic to supersonic. Another advantage is that, the method does not require artificial viscosity since it is naturally diffusive which also ap

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Kayser-Herold, Oliver. "Least-squares methods for the solution of fluid-structure interaction problems." [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=97852408X.

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38

Jiang, J.-S. "Direct methods and least-squares tangent formula in crystal structure determination." Thesis, University of York, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.234963.

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39

Pontaza, Juan Pablo. "Least-squares variational principles and the finite element method: theory, formulations, and models for solid and fluid mechanics." Diss., Texas A&M University, 2003. http://hdl.handle.net/1969.1/288.

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We consider the application of least-squares variational principles and the finite element method to the numerical solution of boundary value problems arising in the fields of solidand fluidmechanics.For manyof these problems least-squares principles offer many theoretical and computational advantages in the implementation of the corresponding finite element model that are not present in the traditional weak form Galerkin finite element model.Most notably, the use of least-squares principles leads to a variational unconstrained minimization problem where stability conditions such as inf-sup co

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Swarup, A. Sri Sakti. "Implicit Least Squares Kinetic Upwind Method (LSKUM) And Implicit LSKUM Based On Entropy Variables (q-LSKUM)." Thesis, Indian Institute of Science, 2000. http://hdl.handle.net/2005/239.

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With increasing demand for computational solutions of fluid dynamical problems, researchers around the world are working on the development of highly robust numerical schemes capable of solving flow problems around complex geometries arising in Aerospace engineering. Also considerable time and effort are devoted to development of convergence acceleration devices, for reducing the computational time required for such numerical solutions. Reduction in run times is very vital for production codes which are used many times in design cycle. In this present work, we consider a numerical scheme calle

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Ku, Wen-Yang. "Lattice preconditioning for the real relaxation based branch and bound method for integer least squares problems." Thesis, McGill University, 2012. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=106555.

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Lattice basis reduction is a powerful tool for solving complex problems both in pure mathematics and practical applications. In this thesis, we use lattice basis reduction as a preconditioning technique to accelerate the real relaxation based branch and bound (RRBB) method for solving integer least squares (ILS) problems. We give theoretical arguments and simulation results to show that applying lattice preconditioning to the RRBB method can greatly reduce the size of the RRBB tree for ordinary ILS problems, making the method more efficient. We then propose new reduction strategies, which are

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Wanchana, Suchada. "Quantitative structure/property relationship modeling of pharmacokinetic properties using genetic algorithm-combined partial least squares method." 京都大学 (Kyoto University), 2003. http://hdl.handle.net/2433/148610.

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43

Chang, Shu-Hao, and 張書豪. "Bayesian-based Partial Least Squares Method." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/33870283050637430689.

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碩士<br>國立交通大學<br>生醫工程研究所<br>98<br>The main purpose of this thesis is to develop a method of analyzing. It is the probability-based multivariate analysis method, names as Bayesian-based partial least squares (Bayesian-based PLS). It combines the advantages of PLS which is widely used method in biomedical spectroscopic analysis, regularization technique and the Bayesian analysis to provide an efficient procedure to avoid the circumstance of overfitting and attain better results when calibrating under noisy data. In the simulated experiments, Bayesian-based PLS is applied to analyze two differen

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44

Chiou, Yu-Ren, and 邱郁仁. "Study on Partial Regularized Least Squares Method." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/47114963708930770517.

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碩士<br>國立交通大學<br>多媒體工程研究所<br>96<br>The main purpose of this thesis is to develop a method of analyzing and reducing the unseen or noisy information from the source data without preprocessing. Here presents a novel learning algorithm—partial regularized least squares (PRLS). It combines the advantages of both the partial least squares (PLS) and regularization technique to provide an efficient procedure to avoid the circumstance of overfitting and attain better results when calibrating under noisy data. In the simulated experiments, PRLS is applied to analyze the three different kinds of simulate

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WANG, WEN-DE, and 王紋德. "Regenerative hybrid arrays using method of least squares." Thesis, 1988. http://ndltd.ncl.edu.tw/handle/62221717770069756958.

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46

Wang, Xiruo. "4-Field Galerkin/least-squares method for polymer flows." Thesis, 2004. http://hdl.handle.net/1911/17743.

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In this thesis, a new finite element method, 4-field Galerkin/Least-Squares method, is presented to solve viscoelastic flow problems. The 4-field GLS naturally includes the SUPG and PSPG terms to stabilize the oscillations caused by advection-dominated terms. In addition, it introduces a new variable L = ∇v, so that the second order derivative of v is avoided, and the basis functions can be chosen as piecewise linear functions. This feature substantially enlarges the space of the basis and weighting functions. The Galerkin terms in this formulation guarantee that the traction term n&mid

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47

"A hybrid incremental gradient method for least squares problems." Massachusetts Institute of Technology, Laboratory for Information and Decision Systems], 1994. http://hdl.handle.net/1721.1/3385.

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48

Hsiao, Tzu-Chien, and 蕭子健. "Multivariate Partial Least Squares Method for Biomedical Spectroscopic Analysis." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/18967838381133750602.

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博士<br>國立陽明大學<br>醫學工程研究所<br>91<br>In this research, a conception of three-layered multivariate analysis structure (input, hidden, and output layer) has been proposed. This concept can be used to compare the performances of Partial Least Squares (PLS) regression and Backpropagation network (BPN), which are widely used methods in biomedical spectroscopic analysis. We also proved that PLS is a special solution of BPN. Based on the fundamental concept of PLS regression, it can be used to interpret some drawbacks of BPN. Such as its long term training epochs, unknown hidden layer, the training resul

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HUANG, CONG-MING, and 黃聰明. "A stable method for solving staircase least squares problems." Thesis, 1990. http://ndltd.ncl.edu.tw/handle/53676739632214832144.

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Shih-WeiYu and 于世偉. "An Application of Least Squares Method for Image Process." Thesis, 2019. http://ndltd.ncl.edu.tw/handle/buug6a.

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碩士<br>國立成功大學<br>數學系應用數學碩博士班<br>107<br>This thesis is to explore how to obtain the affine transformation relationship from two similar images by using the least squares method and the directional derivative to calculate the image, and then compare the images. The comparison method is one of them. The image is subtracted from the other image by the obtained affine transformation relationship. The subtraction is performed by taking the RGB value of each pixel of the image from the first point to the last point of the image. Subtract in order. In the second chapter, when there are more than three

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