On the Krylov subspace methods based on tensor format for positive definite Sylvester tensor equations

Fatemeh Panjeh Ali Beik, Farid Saberi Movahed, Salman Ahmadi-Asl

Результат исследований: Вклад в журналСтатьярецензирование

42 Цитирования (Scopus)

Аннотация

This paper deals with studying some of well-known iterative methods in their tensor forms to solve a Sylvester tensor equation. More precisely, the tensor form of the Arnoldi process and full orthogonalization method are derived by using a product between two tensors. Then tensor forms of the conjugate gradient and nested conjugate gradient algorithms are also presented. Rough estimation of the required number of operations for the tensor form of the Arnoldi process is obtained, which reveals the advantage of handling the algorithms based on tensor format over their classical forms in general. Some numerical experiments are examined, which confirm the feasibility and applicability of the proposed algorithms in practice.

Язык оригиналаАнглийский
Страницы (с-по)444-466
Число страниц23
ЖурналNumerical Linear Algebra with Applications
Том23
Номер выпуска3
DOI
СостояниеОпубликовано - 1 мая 2016
Опубликовано для внешнего пользованияДа

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