Journal ArticleDOI
A weighted pseudoinverse, generalized singular values, and constrained least squares problems
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TLDR
The weighted pseudoinverse theory is used to analyse least squares problems with linear and quadratic constraints as mentioned in this paper, and a numerical algorithm for the computation of the weighted pseudo-inverse is briefly described.Abstract:
The weighted pseudoinverse providing the minimum semi-norm solution of the weighted linear least squares problem is studied. It is shown that it has properties analogous to those of the Moore-Penrose pseudoinverse. The relation between the weighted pseudoinverse and generalized singular values is explained. The weighted pseudoinverse theory is used to analyse least squares problems with linear and quadratic constraints. A numerical algorithm for the computation of the weighted pseudoinverse is briefly described.read more
Citations
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REGULARIZATION TOOLS: A Matlab package for analysis and solution of discrete ill-posed problems
TL;DR: The package REGULARIZATION TOOLS consists of 54 Matlab routines for analysis and solution of discrete ill-posed problems, i.e., systems of linear equations whose coefficient matrix has the properties that its condition number is very large, and its singular values decay gradually to zero.
Journal ArticleDOI
The discrete picard condition of discrete ill-posed problems
TL;DR: In this article, a necessary condition for obtaining good regularized solutions is that the Fourier coefficients of the right-hand side, when expressed in terms of the generalized SVD associated with the regularization problem, on the average decay to zero faster than the generalized singular values.
Journal ArticleDOI
Regularization by Truncated Total Least Squares
TL;DR: This paper proposes and test an iterative algorithm based on Lanczos bidiagonalization for computing truncated TLS solutions and expresses the results in terms of the singular value decomposition of the coefficient matrix rather than the augmented matrix, which leads to insight into the filtering properties of the truncation TLS method as compared to regularized least squares solutions.
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Old and new parameter choice rules for discrete ill-posed problems
TL;DR: This paper studies the performance of known and new approaches to choosing a suitable value of the regularization parameter for the truncated singular value decomposition method and for the LSQR iterative Krylov subspace method in the situation when no accurate estimate of the norm of the error in the data is available.
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.
Book
Generalized inverses: theory and applications
Adi Ben-Israel,T. N. E. Greville +1 more
TL;DR: In this paper, the Moore of the Moore-Penrose Inverse is described as a generalized inverse of a linear operator between Hilbert spaces, and a spectral theory for rectangular matrices is proposed.
Journal ArticleDOI
Generalized Inverse of Matrices and Its Applications
TL;DR: In this article, the generalized inverse of matrices and its applications are discussed and discussed in terms of generalized inverse of matrix and its application in the context of generalization of matrix matrices.