Results 11 to 20 of about 415,219 (164)
Fast Algorithms for Structured Least Squares and Total Least Squares Problems. [PDF]
J Res Natl Inst Stand Technol, 2006 We consider the problem of solving least squares problems involving a matrix M of small displacement rank with respect to two matrices Z 1 and Z 2. We develop formulas for the generators of the matrix M (H) M in terms of the generators of M and show that the Cholesky factorization of the matrix M (H) M can be computed quickly if Z 1 is close to unitary
Kalsi A, O'Leary DP.
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Total least squares methods [PDF]
WIREs Computational Statistics, 2010 Recent advances in total least squares approaches for solving various errors-in-variables modeling problems are reviewed, with emphasis on the following generalizations:1.the use of weighted norms as a measure of the data perturbation size, capturing prior knowledge about uncertainty in the data;2.the addition of constraints on the perturbation to ...
Markovsky, Ivan +2 more
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Regularization by Truncated Total Least Squares [PDF]
SIAM Journal on Scientific Computing, 1997 The truncated total least squares (TLS) technique is investigated. It filters the solution by truncating the small singular values of the TLS matrix. The given iterative algorithm for computing the truncated TLS solution bases on Lanczos bidiagonalization. The algorithm is efficient when the number of retained singular values is small compared with the
Ricardo D. Fierro +3 more
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Orthogonal Projection and Total Least Squares [PDF]
Numerical Linear Algebra with Applications, 1993 AbstractOverdetermined linear systems often arise in applications such as signal processing and modern communication. When the overdetermined system of linear equations AX ≈︁ B has no solution, compatibility may be restored by an orthogonal projection method. The idea is to determine an orthogonal projection matrix P by some method M such that [Ã B̃] =
Ricardo D. Fierro, James R. Bunch
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Tikhonov Regularization and Total Least Squares [PDF]
SIAM Journal on Matrix Analysis and Applications, 1999 The regularized total least squares (TLS) method of the TLS problem is introduced and its regularizing properties are studied. It is also proved that, in certain cases, the new method is superior to standard regularization methods.
Gene H. Golub +2 more
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Overview of total least-squares methods [PDF]
Signal Processing, 2007 We review the development and extensions of the classical total least-squares method and describe algorithms for its generalization to weighted and structured approximation problems. In the generic case, the classical total least-squares problem has a unique solution, which is given in analytic form in terms of the singular value decomposition of the ...
Ivan Markovsky, Sabine Van Huffel
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A Polynomial Fitting Problem: The Orthogonal Distances Method
Mathematics, 2022 The classical curve-fitting problem to relate two variables, x and y, deals with polynomials. Generally, this problem is solved by the least squares method (LS), where the minimization function considers the vertical errors from the data points to the ...
Luis Alberto Cantera-Cantera +4 more
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Total Least Squares Phase Retrieval
IEEE Transactions on Signal Processing, 2022 We address the phase retrieval problem with errors in the sensing vectors. A number of recent methods for phase retrieval are based on least squares (LS) formulations which assume errors in the quadratic measurements. We extend this approach to handle errors in the sensing vectors by adopting the total least squares (TLS) framework that is used in ...
Gupta, Sidharth +2 more
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Total Least Squares Registration of 3D Surfaces
International Journal of Environment and Geoinformatics, 2015 Co-registration of point clouds of partially scanned objects is the first step of the 3D modeling workflow. The aim of co-registration is to merge the overlapping point clouds by estimating the spatial transformation parameters.
Umut Aydar, M. Orhan Altan
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