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Proceedings Shape Modeling Applications, 2004., 2004
In this paper we introduce least-squares meshes: meshes with a prescribed connectivity that approximate a set of control points in a least-squares sense. The given mesh consists of a planar graph with arbitrary connectivity and a sparse set of control points with geometry. The geometry of the mesh is reconstructed by solving a sparse linear system. The
Olga Sorkine, Daniel Cohen-Or
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In this paper we introduce least-squares meshes: meshes with a prescribed connectivity that approximate a set of control points in a least-squares sense. The given mesh consists of a planar graph with arbitrary connectivity and a sparse set of control points with geometry. The geometry of the mesh is reconstructed by solving a sparse linear system. The
Olga Sorkine, Daniel Cohen-Or
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Partial Least Squares Methods: Partial Least Squares Correlation and Partial Least Square Regression
2012Partial least square (PLS) methods (also sometimes called projection to latent structures) relate the information present in two data tables that collect measurements on the same set of observations. PLS methods proceed by deriving latent variables which are (optimal) linear combinations of the variables of a data table.
Hervé, Abdi, Lynne J, Williams
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The Inefficiency of Least Squares
Biometrika, 1975SUMMARY Two criteria are set up to judge the relative performance of the least squares estimator and the best linear unbiased estimator of , in the linear model y = X/, + u, where E(u) = 0, E(uu') = F. The matrices X and r are found so that the relative performance of least squares is worst.
Bloomfield, Peter, Watson, Geoffrey S.
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A Successive Least Squares Method for Structured Total Least Squares
Journal of Computational Mathematics, 2003A new method for Total Least Squares (TLS) problems is presented. It differs from previous approaches and is based on the solution of successive Least Squares problems. The method is quite suitable for Structured TLS (STLS) problems. We study mostly the case of Toeplitz matrices in this paper. The numerical tests illustrate that the method converges to
Yalamov, Plamen Y., Yuan, Jin-yun
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2016
The English version of this paper appeared two years after the Chinese “original”. During the 1950s and early 1960s, DDK visited China several times on exchange programmes.
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The English version of this paper appeared two years after the Chinese “original”. During the 1950s and early 1960s, DDK visited China several times on exchange programmes.
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Information Sciences, 1988
The author discusses three models of fuzzy linear regression function for triangular fuzzy numbers [Fuzzy numbers with triangular shapes, cf. \textit{D. Dubois} and \textit{H. Prade}, Int. J. Syst. Sci. 9, 613-626 (1978; Zbl 0383.94045)]. Formulas are deduced by the least-squares method.
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The author discusses three models of fuzzy linear regression function for triangular fuzzy numbers [Fuzzy numbers with triangular shapes, cf. \textit{D. Dubois} and \textit{H. Prade}, Int. J. Syst. Sci. 9, 613-626 (1978; Zbl 0383.94045)]. Formulas are deduced by the least-squares method.
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Least squares and total least squares methods in image restoration
1997Image restoration is the process of removing or minimizing degradations (blur) in an image. Mathematically, it can be modeled as a discrete ill-posed problem Hf=g, where H is a matrix of large dimension representing the blurring phenomena, and g is a vector representing the observed image.
Julie Kamm, James G. Nagy
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Computers & Graphics, 1978
Abstract The method of least-squares is intended to fit a function to a set of data points closely, so as to satisfy a particular criterion of closeness. The approximating function can be taken to be a linear combination of linearly independent functions of an independent variable.
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Abstract The method of least-squares is intended to fit a function to a set of data points closely, so as to satisfy a particular criterion of closeness. The approximating function can be taken to be a linear combination of linearly independent functions of an independent variable.
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Collinearity and Total Least Squares
SIAM Journal on Matrix Analysis and Applications, 1994The least squares (LS) and total least squares (TLS) methods are commonly used to solve the overdetermined system of equations $Ax \approx b$. The main objective of this paper is to examine TLS when A is nearly rank deficient by outlining its differences and similarities to the well-known truncated LS method.
Ricardo D. Fierro, James R. Bunch
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1981
In the next three chapters we shall discuss a particular form of statistical model, which gives rise to simple statistical methods of very wide applicability. The basic model has been mentioned in Section 2.1, Equation (2.2), see also Example 3.12, but the following example illustrates how it arises in practice.
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In the next three chapters we shall discuss a particular form of statistical model, which gives rise to simple statistical methods of very wide applicability. The basic model has been mentioned in Section 2.1, Equation (2.2), see also Example 3.12, but the following example illustrates how it arises in practice.
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