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

Salman Ahmadi-Asl, Fatemeh Panjeh Ali Beik

Результат исследований: Вклад в журналСтатьярецензирование

7 Цитирования (Scopus)

Аннотация

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 A1X+(A1X)ηH+B1YB1ηH+C1ZC1ηH=D1,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 η-Hermitian or η-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.

Язык оригиналаАнглийский
Страницы (с-по)95-127
Число страниц33
ЖурналJournal of Applied Mathematics and Computing
Том53
Номер выпуска1-2
DOI
СостояниеОпубликовано - 1 февр. 2017
Опубликовано для внешнего пользованияДа

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