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Journal of Applied Mathematics and Computing
Erschienen in: Journal of Applied Mathematics and Computing 1-2/2017

17.11.2015 | Original Research

Iterative algorithms for least-squares solutions of a quaternion matrix equation

verfasst von: Salman Ahmadi-Asl, Fatemeh Panjeh Ali Beik

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2017

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Abstract

This paper deals with developing four efficient algorithms (including the conjugate gradient least-squares, least-squares with QR factorization, least-squares minimal residual and Paige algorithms) to numerically find the (least-squares) solutions of the following (in-) consistent quaternion matrix equation
$$\begin{aligned} {A_1}X + {\left( {{A_1}X} \right) ^{\eta H}} + {B_1}YB_1^{\eta H} + {C_1}ZC_1^{\eta H} = {D_1}, \end{aligned}$$
in which the coefficient matrices are large and sparse. More precisely, we construct four efficient iterative algorithms for determining triple least-squares solutions (X, Y, Z) such that X may have a special assumed structure, Y and Z can be either \(\eta \)-Hermitian or \(\eta \)-anti-Hermitian matrices. In order to speed up the convergence of the offered algorithms for the case that the coefficient matrices are possibly ill-conditioned, a preconditioned technique is employed. Some numerical test problems are examined to illustrate the effectiveness and feasibility of presented algorithms.
Vorheriger Artikel Approximating the traveling wavefront for a nonlocal delayed reaction-diffusion equation
Nächster Artikel Existence of solutions for fractional differential equations with nonlocal and average type integral boundary conditions

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Metadaten
Titel
Iterative algorithms for least-squares solutions of a quaternion matrix equation
verfasst von
Salman Ahmadi-Asl
Fatemeh Panjeh Ali Beik
Publikationsdatum
17.11.2015
Verlag
Springer Berlin Heidelberg
Erschienen in
Journal of Applied Mathematics and Computing / Ausgabe 1-2/2017
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-015-0959-6

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