LSLQ: An Iterative Method for Linear Least-Squares with an Error Minimization Property

2019 ◽  
Vol 40 (1) ◽  
pp. 254-275 ◽  
Author(s):  
Ron Estrin ◽  
Dominique Orban ◽  
Michael A. Saunders
Keyword(s):  
Iterative Method ◽  
Least Squares ◽  
Error Minimization ◽  
Linear Least Squares ◽  
Minimization Property

scholarly journals On weighted Strand’s iteration

2018 ◽  
Vol 34 (2) ◽  
pp. 183-190
Author(s):  
D. CARP ◽  
◽  
C. POPA ◽  
T. PRECLIK ◽  
U. RUDE ◽  
...  
Keyword(s):  
Iterative Method ◽  
Least Squares ◽  
Numerical Approximation ◽  
Iterative Algorithms ◽  
Linear Least Squares ◽  
Minimal Norm ◽  
Least Squares Problem ◽  
Minimal Norm Solution ◽  
Linear Least Squares Problem

In this paper we present a generalization of Strand’s iterative method for numerical approximation of the weighted minimal norm solution of a linear least squares problem. We prove convergence of the extended algorithm, and show that previous iterative algorithms proposed by L. Landweber, J. D. Riley and G. H. Golub are particular cases of it.

LNLQ: An Iterative Method for Least-Norm Problems with an Error Minimization Property

2019 ◽  
Vol 40 (3) ◽  
pp. 1102-1124 ◽  
Author(s):  
Ron Estrin ◽  
Dominique Orban ◽  
Michael A. Saunders
Keyword(s):  
Iterative Method ◽  
Error Minimization ◽  
Minimization Property

THE REALIZATION OF THE ITERATIVE METHOD OF THE LEAST SQUARES FOR THE ESTIMATION OF STATIC OBJECT PARAMETERS IN MATLAB ENVIRONMENT

2017 ◽  
pp. 28-36
Author(s):  
Galina Vasil’evna Troshina ◽  
Alexander Aleksandrovich Voevoda
Keyword(s):  
Parameter Estimation ◽  
Iterative Method ◽  
Least Squares ◽  
Input Signal ◽  
Layer Structure ◽  
Estimation Procedure ◽  
Parameter Estimation Procedure ◽  
Noise Simulation ◽  
Static Object ◽  
Object Parameters

It was suggested to use the system model working in real time for an iterative method of the parameter estimation. It gives the chance to select a suitable input signal, and also to carry out the setup of the object parameters. The object modeling for a case when the system isn't affected by the measurement noises, and also for a case when an object is under the gaussian noise was executed in the MatLab environment. The superposition of two meanders with different periods and single amplitude is used as an input signal. The model represents the three-layer structure in the MatLab environment. On the most upper layer there are units corresponding to the simulation of an input signal, directly the object, the unit of the noise simulation and the unit for the parameter estimation. The second and the third layers correspond to the simulation of the iterative method of the least squares. The diagrams of the input and the output signals in the absence of noise and in the presence of noise are shown. The results of parameter estimation of a static object are given. According to the results of modeling, the algorithm works well even in the presence of significant measurement noise. To verify the correctness of the work of an algorithm the auxiliary computations have been performed and the diagrams of the gain behavior amount which is used in the parameter estimation procedure have been constructed. The entry conditions which are necessary for the work of an iterative method of the least squares are specified. The understanding of this algorithm functioning principles is a basis for its subsequent use for the parameter estimation of the multi-channel dynamic objects.

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