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Journal articles on the topic 'The Method of Least Squares'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

JIANG, BO-NAN. "LEAST-SQUARES MESHFREE COLLOCATION METHOD." International Journal of Computational Methods 09, no. 02 (2012): 1240031. http://dx.doi.org/10.1142/s0219876212400312.

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A least-squares meshfree collocation method is presented. The method is based on the first-order differential equations in order to result in a better conditioned linear algebraic equations, and to obtain the primary variables (displacements) and the dual variables (stresses) simultaneously with the same accuracy. The moving least-squares approximation is employed to construct the shape functions. The sum of squared residuals of both differential equations and boundary conditions at nodal points is minimized. The present method does not require any background mesh and additional evaluation poi

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2

Jiang, Bo-Nan. "On the least-squares method." Computer Methods in Applied Mechanics and Engineering 152, no. 1-2 (1998): 239–57. http://dx.doi.org/10.1016/s0045-7825(97)00192-8.

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3

Zhang, Xiong, Xiao‐Hu Liu, Kang‐Zu Song, and Ming‐Wan Lu. "Least‐squares collocation meshless method." International Journal for Numerical Methods in Engineering 51, no. 9 (2001): 1089–100. http://dx.doi.org/10.1002/nme.200.

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4

Park, Sang‐Hoon, and Sung‐Kie Youn. "The least‐squares meshfree method." International Journal for Numerical Methods in Engineering 52, no. 9 (2001): 997–1012. http://dx.doi.org/10.1002/nme.248.

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5

D'Antona, G. "The full least-squares method." IEEE Transactions on Instrumentation and Measurement 52, no. 1 (2003): 189–96. http://dx.doi.org/10.1109/tim.2003.809489.

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6

Pan, X. F., X. Zhang, and M. W. Lu. "Meshless Galerkin least-squares method." Computational Mechanics 35, no. 3 (2004): 182–89. http://dx.doi.org/10.1007/s00466-004-0615-8.

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7

Frank, Ildiko E. "Intermediate least squares regression method." Chemometrics and Intelligent Laboratory Systems 1, no. 3 (1987): 233–42. http://dx.doi.org/10.1016/0169-7439(87)80067-9.

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8

Clack, Jhules, Donald A. French, and Mauricio Osorio. "Error analysis of a least squares pseudo-derivative moving least squares method." Proyecciones (Antofagasta) 36, no. 3 (2017): 435–48. http://dx.doi.org/10.4067/s0716-09172017000300435.

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9

Liu, Qiaohua, and Minghui Wang. "On the weighting method for mixed least squares-total least squares problems." Numerical Linear Algebra with Applications 24, no. 5 (2017): e2094. http://dx.doi.org/10.1002/nla.2094.

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10

Gorlachev, I. D., B. B. Knyazev, A. Kuketayev, and F. M. Pen’kov. "Properties of integral least squares method." Bulletin of the Russian Academy of Sciences: Physics 73, no. 2 (2009): 245–48. http://dx.doi.org/10.3103/s1062873809020269.

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11

Konopatskiy, Ye V. "GEOMETRIC MEANING OF LEAST SQUARES METHOD." Vestnik komp'iuternykh i informatsionnykh tekhnologii, no. 183 (September 2019): 11–18. http://dx.doi.org/10.14489/vkit.2019.09.pp.011-018.

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The geometric interpretation of the least squares method is presents. At the same time, one of its possible generalizations to multidimensional space is proposed. This approach makes it possible to expand the capabilities one of the key methods of multidimensional approximation and effectively use it for geometric modeling of multifactor processes and phenomena. The analytical description of the proposed method is performed using point equations. The geometric interpretation of the generalized least squares method, which consists in determining the linear surface of the minimum width between t

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12

Musivand-Arzanfudi, M., and H. Hosseini-Toudeshky. "Moving least-squares finite element method." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 221, no. 9 (2007): 1019–36. http://dx.doi.org/10.1243/09544062jmes463.

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A new computational method here called moving least-squares finite element method (MLSFEM) is presented, in which the shape functions of the parametric elements are constructed using moving least-squares approximation. While preserving some excellent characteristics of the meshless methods such as elimination of the volumetric locking in near-incompressible materials and giving accurate strains and stresses near the boundaries of the problem, the computational time is decreased by constructing the meshless shape functions in the stage of creating parametric elements and then utilizing them for

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13

Apagyi, Barnabás, and Károly Ladányi. "Least-squares method in scattering theory." Physical Review A 33, no. 1 (1986): 182–90. http://dx.doi.org/10.1103/physreva.33.182.

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14

苗, 嘉兴. "Discussion on the Least-Squares Method." Pure Mathematics 09, no. 04 (2019): 486–91. http://dx.doi.org/10.12677/pm.2019.94065.

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15

TAKAMASU, Kiyoshi. "Least Squares Method for Precision Measurement." Journal of the Japan Society for Precision Engineering 76, no. 10 (2010): 1130–33. http://dx.doi.org/10.2493/jjspe.76.1130.

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16

Bochev, Pavel, and Marc Gerritsma. "A spectral mimetic least-squares method." Computers & Mathematics with Applications 68, no. 11 (2014): 1480–502. http://dx.doi.org/10.1016/j.camwa.2014.09.014.

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17

Abdulle, Assyr, and Gerhard Wanner. "200 years of least squares method." Elemente der Mathematik 57, no. 2 (2002): 45–60. http://dx.doi.org/10.1007/pl00000559.

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18

Kamiński, Marcin. "Least squares stochastic Boundary Element Method." Engineering Analysis with Boundary Elements 35, no. 5 (2011): 776–84. http://dx.doi.org/10.1016/j.enganabound.2011.01.004.

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19

Franca, Leopoldo Penna, and Eduardo Gomes Dutra Do Carmo. "The Galerkin gradient least-squares method." Computer Methods in Applied Mechanics and Engineering 74, no. 1 (1989): 41–54. http://dx.doi.org/10.1016/0045-7825(89)90085-6.

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20

Zorkaltsev, V. I., and E. V. Gubiy. "Chebyshev Approximations by Least Squares Method." Bulletin of Irkutsk State University. Series Mathematics 33 (2020): 3–19. http://dx.doi.org/10.26516/1997-7670.2020.33.3.

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21

Sheynin, Oscar. "Graphical least squares method and Gauss." Śląski Przegląd Statystyczny 18, no. 24 (2020): 325–26. http://dx.doi.org/10.15611/sps.2020.18.24.

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22

Iwahara, Mitsuo, and Akio Nagamatsu. "An Optimization Method with Pseudo-Least-Squares Method." Transactions of the Japan Society of Mechanical Engineers Series C 61, no. 587 (1995): 2683–90. http://dx.doi.org/10.1299/kikaic.61.2683.

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23

YUKUTAKE, Kiyoshi, and Atsushi YOSHIMOTO. "Analysis of Lumber Demand and Supply in Japan : Price Elasticities by the Ordinary Least Squares Method, Two Stage Least Squares Method and Three Stage Least Squares Method." Japanese Journal of Forest Planning 36, no. 2 (2002): 81–98. http://dx.doi.org/10.20659/jjfp.36.2_81.

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24

Araveeporn, Autcha. "Comparing Parameter Estimation of Random Coefficient Autoregressive Model by Frequentist Method." Mathematics 8, no. 1 (2020): 62. http://dx.doi.org/10.3390/math8010062.

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This paper compares the frequentist method that consisted of the least-squares method and the maximum likelihood method for estimating an unknown parameter on the Random Coefficient Autoregressive (RCA) model. The frequentist methods depend on the likelihood function that draws a conclusion from observed data by emphasizing the frequency or proportion of the data namely least squares and maximum likelihood methods. The method of least squares is often used to estimate the parameter of the frequentist method. The minimum of the sum of squared residuals is found by setting the gradient to zero.

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25

Gatto, Marta, and Fabio Marcuzzi. "Unbiased Least-Squares Modelling." Mathematics 8, no. 6 (2020): 982. http://dx.doi.org/10.3390/math8060982.

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In this paper we analyze the bias in a general linear least-squares parameter estimation problem, when it is caused by deterministic variables that have not been included in the model. We propose a method to substantially reduce this bias, under the hypothesis that some a-priori information on the magnitude of the modelled and unmodelled components of the model is known. We call this method Unbiased Least-Squares (ULS) parameter estimation and present here its essential properties and some numerical results on an applied example.

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26

Yeniay, Özgür, Öznur İşçi, Atilla Göktaş, and M. Niyazi Çankaya. "Time Scale in Least Square Method." Abstract and Applied Analysis 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/354237.

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Study of dynamic equations in time scale is a new area in mathematics. Time scale tries to build a bridge between real numbers and integers. Two derivatives in time scale have been introduced and called as delta and nabla derivative. Delta derivative concept is defined as forward direction, and nabla derivative concept is defined as backward direction. Within the scope of this study, we consider the method of obtaining parameters of regression equation of integer values through time scale. Therefore, we implemented least squares method according to derivative definition of time scale and obtai

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27

Lieb, Shannon G. "Simplex Method of Nonlinear Least-Squares - A Logical Complementary Method to Linear Least-Square Analysis of Data." Journal of Chemical Education 74, no. 8 (1997): 1008. http://dx.doi.org/10.1021/ed074p1008.

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28

Jin, Xi, Xing Zhang, Kaifeng Rao, Liang Tang, and Qiwei Xie. "Semi-supervised partial least squares." International Journal of Wavelets, Multiresolution and Information Processing 18, no. 03 (2020): 2050014. http://dx.doi.org/10.1142/s0219691320500149.

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Traditional supervised dimensionality reduction methods can establish a better model often under the premise of a large number of samples. However, in real-world applications where labeled data are scarce, traditional methods tend to perform poorly because of overfitting. In such cases, unlabeled samples could be useful in improving the performance. In this paper, we propose a semi-supervised dimensionality reduction method by using partial least squares (PLS) which we call semi-supervised partial least squares (S2PLS). To combine the labeled and unlabeled samples into a S2PLS model, we first

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29

Jeng, Yih Nen, and Wu Sheng Lin. "Weighted least squares method of grid generation." AIAA Journal 33, no. 2 (1995): 364–65. http://dx.doi.org/10.2514/3.12396.

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30

Paris, Quirino. "The Dual of the Least-Squares Method." Open Journal of Statistics 05, no. 07 (2015): 658–64. http://dx.doi.org/10.4236/ojs.2015.57067.

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31

Gu, Le Min. "P-Least Squares Method of Curve Fitting." Advanced Materials Research 699 (May 2013): 885–92. http://dx.doi.org/10.4028/www.scientific.net/amr.699.885.

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P-Least Squares (P-LS) method is Least Squares (LS) method promotion, based on the criteria of error -squares minimal to select parameter , namely satisfies following constitute the curve-fitting method. Due to the arbitrariness of the number , P-LS method has a wide field of application, when , P-LS approximation translated Chebyshev optimal approximation. This paper discusses the general principles of P-LS method; provides a way to realize the general solution of P-LS approximation. P-Least Squares method not only has significantly reduces the maximum error, also has solved the problems of C

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32

NAKAMURA, Osamu, Satoshi KAWATA, and Shigeo MINAMI. "Superresolving deconvolution by Nonnegative Least Squares Method." Journal of the Spectroscopical Society of Japan 35, no. 3 (1986): 218–24. http://dx.doi.org/10.5111/bunkou.35.218.

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33

Yu.M., Neyman, and Sugaipova L.S. "On computational scheme of least squares method." Geodesy and Aerophotosurveying 63, no. 1 (2019): 21–31. http://dx.doi.org/10.30533/0536-101x-2019-63-1-21-31.

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34

Soloviov, Vladimir. "Minimax estimation and the least squares method." Stochastics and Stochastic Reports 42, no. 3-4 (1993): 209–23. http://dx.doi.org/10.1080/17442509308833820.

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35

Léger, Michel, Muriel Thibaut, Jean-Pierre Gratier, and Jean-Marie Morvan. "A least-squares method for multisurface unfolding." Journal of Structural Geology 19, no. 5 (1997): 735–43. http://dx.doi.org/10.1016/s0191-8141(97)85678-7.

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36

Choi, Seung Hoe, and Jin Hee Yoon. "General fuzzy regression using least squares method." International Journal of Systems Science 41, no. 5 (2010): 477–85. http://dx.doi.org/10.1080/00207720902774813.

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37

Rosenholm, D. "LEAST SQUARES MATCHING METHOD: SOME EXPERIMENTAL RESULTS." Photogrammetric Record 12, no. 70 (2006): 493–512. http://dx.doi.org/10.1111/j.1477-9730.1987.tb00598.x.

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38

Patwardhan, A. A., M. N. Karim, and R. Shah. "Controller tuning by a least-squares method." AIChE Journal 33, no. 10 (1987): 1735–37. http://dx.doi.org/10.1002/aic.690331018.

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39

Nja, M. "A Modified Iterative Weighted Least Squares Method." British Journal of Mathematics & Computer Science 4, no. 6 (2014): 849–57. http://dx.doi.org/10.9734/bjmcs/2014/7442.

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40

Deshpande, Suresh, V. Ramesh, Keshav Malagi, and Konark Arora. "Least squares Kinetic Upwind Mesh-free Method." Defence Science Journal 60, no. 6 (2010): 583–97. http://dx.doi.org/10.14429/dsj.60.579.

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41

Lucas, T. N., and A. R. Munro. "Model reduction by generalised least-squares method." Electronics Letters 27, no. 15 (1991): 1383. http://dx.doi.org/10.1049/el:19910869.

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42

Lira, I. "Curve adjustment by the least-squares method." Metrologia 37, no. 6 (2000): 677–81. http://dx.doi.org/10.1088/0026-1394/37/6/5.

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43

Slabospitskii, A. S. "Convergence conditions of the least squares method." Journal of Mathematical Sciences 72, no. 3 (1994): 3076–79. http://dx.doi.org/10.1007/bf01259474.

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44

Sharapudinov, I. I. "Convergence of the method of least squares." Mathematical Notes 53, no. 3 (1993): 335–44. http://dx.doi.org/10.1007/bf01207722.

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45

Ambrosio, L., P. D'Ancona, and S. Mortola. "Gamma-convergence and the least squares method." Annali di Matematica Pura ed Applicata 166, no. 1 (1994): 101–27. http://dx.doi.org/10.1007/bf01765630.

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46

Menke, William. "Review of the Generalized Least Squares Method." Surveys in Geophysics 36, no. 1 (2014): 1–25. http://dx.doi.org/10.1007/s10712-014-9303-1.

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47

Cui, Xiaoke, Ken Hayami, and Jun-Feng Yin. "Greville’s method for preconditioning least squares problems." Advances in Computational Mathematics 35, no. 2-4 (2011): 243–69. http://dx.doi.org/10.1007/s10444-011-9171-x.

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48

Tamai, Tasuku, and Seiichi Koshizuka. "Least squares moving particle semi-implicit method." Computational Particle Mechanics 1, no. 3 (2014): 277–305. http://dx.doi.org/10.1007/s40571-014-0027-2.

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49

Verotta, Davide. "An inequality-constrained least-squares deconvolution method." Journal of Pharmacokinetics and Biopharmaceutics 17, no. 2 (1989): 269–89. http://dx.doi.org/10.1007/bf01059031.

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50

Cai, Zhiqiang, and Binghe Chen. "Least-squares method for the Oseen equation." Numerical Methods for Partial Differential Equations 32, no. 4 (2016): 1289–303. http://dx.doi.org/10.1002/num.22055.

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