Iterative Methods for Least Squares Problem in Split Quaternionic Mechanics

The deteriorating effect of old history in asynchronous implementations of Jacobi-type iterative methods applied to linear least squares problem is well documented. A partially asynchronous algorithm is developed which employs a combination of synchronization, a relaxation parameter and an aggregation of variables. It is shown by numerical experiments that this combined effort to decrease the effect of old history is effective.

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Perturbation analysis and condition numbers of mixed least squares-scaled total least squares problem

Numerical Algorithms ◽

10.1007/s11075-021-01151-4 ◽

2021 ◽

Author(s):

Pingping Zhang ◽

Qun Wang

Keyword(s):

Least Squares ◽

Perturbation Analysis ◽

Total Least Squares ◽

Condition Numbers ◽

Least Squares Problem

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A Unitarily Constrained Total Least Squares Problem in Signal Processing

SIAM Journal on Matrix Analysis and Applications ◽

10.1137/0613046 ◽

1992 ◽

Vol 13 (3) ◽

pp. 729-745 ◽

Cited By ~ 37

Author(s):

K. S. Arun

Keyword(s):

Signal Processing ◽

Least Squares ◽

Total Least Squares ◽

Least Squares Problem

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An efficient method for solving a matrix least squares problem over a matrix inequality constraint

Computational Optimization and Applications ◽

10.1007/s10589-015-9783-z ◽

2015 ◽

Vol 63 (2) ◽

pp. 393-423 ◽

Cited By ~ 6

Author(s):

Jiao-fen Li ◽

Wen Li ◽

Ru Huang

Keyword(s):

Least Squares ◽

Efficient Method ◽

Inequality Constraint ◽

Matrix Inequality ◽

Least Squares Problem

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The Least Squares Problem

Compact Textbooks in Mathematics - Elementary Numerical Mathematics for Programmers and Engineers ◽

10.1007/978-3-319-44660-8_4 ◽

2016 ◽

pp. 69-84

Author(s):

Gisbert Stoyan ◽

Agnes Baran

Keyword(s):

Least Squares ◽

Least Squares Problem

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Solution of the Adiabatic Sound Wave Equation as a Nonlinear Least Squares Problem

International Journal of Thermophysics ◽

10.1007/s10765-018-2479-8 ◽

2019 ◽

Vol 40 (2) ◽

Author(s):

Muhamed Bijedić ◽

Sabina Begić

Keyword(s):

Wave Equation ◽

Least Squares ◽

Sound Wave ◽

Nonlinear Least Squares ◽

Least Squares Problem ◽

Nonlinear Least Squares Problem

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A regularized strong duality for nonsymmetric semidefinite least squares problem

Optimization Letters ◽

10.1007/s11590-010-0233-7 ◽

2010 ◽

Vol 5 (4) ◽

pp. 665-682 ◽

Cited By ~ 1

Author(s):

Yingnan Wang ◽

Naihua Xiu ◽

Ziyan Luo

Keyword(s):

Least Squares ◽

Strong Duality ◽

Least Squares Problem

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Perturbation of the least squares problem

Linear Algebra and its Applications ◽

10.1016/0024-3795(90)90316-5 ◽

1990 ◽

Vol 141 ◽

pp. 177-182 ◽

Cited By ~ 15

Author(s):

Musheng Wei

Keyword(s):

Least Squares ◽

Least Squares Problem

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A fast algorithm for solving the Sylvester structured total least squares problem

Signal Processing ◽

10.1016/j.sigpro.2007.03.001 ◽

2007 ◽

Vol 87 (10) ◽

pp. 2313-2319 ◽

Cited By ~ 3

Author(s):

Bingyu Li ◽

Zhuojun Liu ◽

Lihong Zhi

Keyword(s):

Least Squares ◽

Fast Algorithm ◽

Total Least Squares ◽

Least Squares Problem ◽

Structured Total Least Squares

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On weighted Strand’s iteration

Carpathian Journal of Mathematics ◽

10.37193/cjm.2018.02.06 ◽

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.

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