Results 11 to 20 of about 1,514,703 (285)
Convex Total Least Squares [PDF]
CoRR, 2014 We study the total least squares (TLS) problem that generalizes least squares regression by allowing measurement errors in both dependent and independent variables. TLS is widely used in applied fields including computer vision, system identification and
Malioutov, Dmitry M., Slavov, Nikolai
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On weighted structured total least squares [PDF]
, 2006 In this contribution we extend the result of (Markovsky et. al, SIAM J. of Matrix Anal. and Appl., 2005) to the case of weighted cost function. It is shown that the computational complexity of the proposed algorithm is preserved linear in the sample size
G. Golub +4 more
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A Recursive Restricted Total Least-squares Algorithm
IEEE Transactions on Signal Processing, 2014 International audienceWe show that the generalized total least squares (GTLS) problem with a singular noise covariance matrix is equivalent to the restricted total least squares (RTLS) problem and propose a recursive method for its numerical solution ...
Gauterin, Frank +3 more
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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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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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Global total least squares modeling of multivariable time series [PDF]
, 1995 Presents a novel approach for the modeling of multivariable time series. The model class consists of linear systems, i.e., the solution sets of linear difference equations.
Heij, Christiaan, Roorda, Berend
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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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