GLOBAL CONVERGENCE OF RTLSQEP: A SOLVER OF REGULARIZED TOTAL LEAST SQUARES PROBLEMS VIA QUADRATIC EIGENPROBLEMS

The total least squares (TLS) method is a successful approach for linear problems if both the matrix and the right hand side are contaminated by some noise. In a recent paper Sima, Van Huffel and Golub suggested an iterative method for solving regularized TLS problems, where in each iteration step a quadratic eigenproblem has to be solved. In this paper we prove its global convergence, and we present an efficient implementation using an iterative projection method with thick updates.

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An efficient Gauss–Newton algorithm for solving regularized total least squares problems

Numerical Algorithms ◽

10.1007/s11075-021-01145-2 ◽

2021 ◽

Author(s):

Hossein Zare ◽

Masoud Hajarian

Keyword(s):

Least Squares ◽

Total Least Squares ◽

Least Squares Problems ◽

Newton Algorithm ◽

Regularized Total Least Squares

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TOTAL LEAST SQUARES FOR ESTIMATION OF THE GROSS OUTPUT VECTOR

Russian science: actual researches and developments,Part 1 ◽

10.46554/russian.science-2020.03-1-83/85 ◽

2020 ◽

Author(s):

Dmitriy Vladimirovich Ivanov ◽

Keyword(s):

Least Squares ◽

Least Squares Method ◽

Direct Costs ◽

Total Least Squares ◽

Test Cases ◽

Output Vector ◽

Final Consumption ◽

The Matrix

The article proposes the estimation of the gross output vector in the presence of errors in the matrix of direct costs and the final consumption vector. The article suggests the use of the total least squares method for estimating the gross output vector. Test cases showed that the accuracy of the proposed estimates of the gross output vector is higher than the accuracy of the estimates obtained using the classical least squares method (OLS).

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Position Estimation of Single Camera Visual System Based on Total Least Squares Algorithm

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.239-240.1352 ◽

2012 ◽

Vol 239-240 ◽

pp. 1352-1355

Author(s):

Jing Zhou ◽

Yin Han Gao ◽

Chang Yin Liu ◽

Ji Zhi Li

Keyword(s):

Visual System ◽

Least Squares ◽

Total Least Squares ◽

Position Estimation ◽

Feature Points ◽

Perspective Theory ◽

Optical Feature ◽

The Matrix ◽

Least Squares Algorithm ◽

Set Up

The position estimation of optical feature points of visual system is the focus factor of the precision of system. For this problem , to present the Total Least Squares Algorithm . Firstly , set up the measurement coordinate system and 3D model between optical feature points, image points and the position of camera according to the position relation ; Second , build the matrix equations between optical feature points and image points ; Then apply in the total least squares to have an optimization calculation ; Finally apply in the coordinate measuring machining to have a simulation comparison experiment , the results indicate that the standard tolerance of attitude coordinate calculated by total least squares is 0.043mm, it validates the effectiveness; Compare with the traditional method based on three points perspective theory, measure the standard gauge of 500mm; the standard tolerance of traditional measurement system is 0.0641mm, the standard tolerance of Total Least Squares Algorithm is 0.0593mm; The experiment proves the Total Least Squares Algorithm is effective and has high precision.

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