Total least squares solution for compositional data using linear models

2010 ◽  
Vol 37 (7) ◽  
pp. 1137-1152 ◽  
Author(s):  
Eva Fišerová ◽  
Karel Hron
Keyword(s):  
Least Squares ◽  
Linear Models ◽  
Compositional Data ◽  
Total Least Squares ◽  
Least Squares Solution

scholarly journals A Representation of Nonhomogeneous Quadratic Forms with Application to the Least Squares Solution

2011 ◽  
Vol 2011 ◽  
pp. 1-5 ◽  
Author(s):  
Czesław Stępniak
Keyword(s):  
Least Squares ◽  
Quadratic Forms ◽  
Differential Calculus ◽  
Linear Models ◽  
Linear Equations ◽  
Algebraic Approach ◽  
System Of Linear Equations ◽  
Least Squares Solution ◽  
Inconsistent System ◽  
Usual Solution

The least squares problem appears, among others, in linear models, and it refers to inconsistent system of linear equations. A crucial question is how to reduce the least squares solution in such a system to the usual solution in a consistent one. Traditionally, this is reached by differential calculus. We present a purely algebraic approach to this problem based on some identities for nonhomogeneous quadratic forms.

scholarly journals A Stochastic Total Least Squares Solution of Adaptive Filtering Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Shazia Javed ◽  
Noor Atinah Ahmad
Keyword(s):  
Least Squares ◽  
Adaptive Filtering ◽  
Optimal Solution ◽  
Total Least Squares ◽  
Mean Square ◽  
Least Mean Square ◽  
Least Squares Solution ◽  
Input And Output ◽  
Unknown System ◽  
Filtering Problem

An efficient and computationally linear algorithm is derived for total least squares solution of adaptive filtering problem, when both input and output signals are contaminated by noise. The proposed total least mean squares (TLMS) algorithm is designed by recursively computing an optimal solution of adaptive TLS problem by minimizing instantaneous value of weighted cost function. Convergence analysis of the algorithm is given to show the global convergence of the proposed algorithm, provided that the stepsize parameter is appropriately chosen. The TLMS algorithm is computationally simpler than the other TLS algorithms and demonstrates a better performance as compared with the least mean square (LMS) and normalized least mean square (NLMS) algorithms. It provides minimum mean square deviation by exhibiting better convergence in misalignment for unknown system identification under noisy inputs.

scholarly journals The Constrained Total Least Squares Solution for Virtual Reference Feedback Tuning

2020 ◽  
Vol 53 (2) ◽  
pp. 3983-3988
Author(s):  
Cristiane Silva Garcia ◽  
Alexandre Sanfelici Bazanella
Keyword(s):  
Least Squares ◽  
Total Least Squares ◽  
Virtual Reference ◽  
Least Squares Solution
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