The general linear model and the generalized singular value decomposition
TLDR
In this paper, a new derivation is given for the generalized singular value decomposition of two matrices X and F having the same number of rows, which reveals the structure of the general Gauss-Markov linear model ( y, X β, σ 2 FF′ ), and exhibits the structure and solution of the generalized linear least squares problem used to provide the best linear unbiased estimator for the model.About:
This article is published in Linear Algebra and its Applications.The article was published on 1985-10-01 and is currently open access. It has received 27 citations till now. The article focuses on the topics: Generalized singular value decomposition & Singular value decomposition.read more
Citations
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A higher-order generalized singular value decomposition for comparison of global mRNA expression from multiple organisms.
TL;DR: It is found that the approximately common HO GSVD subspace represents the cell-cycle mRNA expression oscillations, which is similar among the datasets, and simultaneous reconstruction in the common subspace removes the experimental artifacts, which are dissimilar, from the datasets.
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Computing the generalized singular value decomposition
Zhaojun Bai,James Demmel +1 more
TL;DR: A new numerical method for computing the GSVD of two matrices A and B is presented, a variation on Paige''s method, which differs from previous algorithms in guaranteeing both backward stability and convergence.
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A Tangent Algorithm for Computing the Generalized Singular Value Decomposition
TL;DR: Two new algorithms for floating-point computation of the generalized singular values of a real pair of full column rank matrices and for Floating-point solution of the summarized eigenvalue problem with symmetric, positive definite matrices of H and M are presented.
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The singular value decomposition in multivariate statistics
TL;DR: To Gene Golub who has done so much to encourage and advance the use of stable numerical techniques in multivariate statistics as mentioned in this paper, we would like to extend our thanks to Gene.
References
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Book
Solving least squares problems
TL;DR: Since the lm function provides a lot of features it is rather complicated so it is going to instead use the function lsfit as a model, which computes only the coefficient estimates and the residuals.
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Solving Least Squares Problems
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The Rotation of Eigenvectors by a Perturbation. III
Chandler Davis,William Kahan +1 more
TL;DR: In this article, the difference between the two subspaces is characterized in terms of certain angles through which one subspace must be rotated in order most directly to reach the other, and Sharp bounds upon trigonometric functions of these angles are obtained from the gap and from bounds upon either the perturbation or a computable residual.
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Generalizing the Singular Value Decomposition
TL;DR: Two generalizations of the singular value decomposition are given in this article, and these generalizations provided a unified way of regarding certain matrix problems and the numerical techniques which are used to solve them.