Pregled bibliografske jedinice broj: 993468
On the convergence of complex Jacobi methods
On the convergence of complex Jacobi methods // Linear and multilinear algebra, 69 (2021), 3; 489-514 doi:10.1080/03081087.2019.1604622 (međunarodna recenzija, članak, znanstveni)
CROSBI ID: 993468 Za ispravke kontaktirajte CROSBI podršku putem web obrasca
Naslov
On the convergence of complex Jacobi methods
Autori
Hari, Vjeran ; Begović Kovač, Erna
Izvornik
Linear and multilinear algebra (0308-1087) 69
(2021), 3;
489-514
Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni
Ključne riječi
Complex Jacobi method ; complex Jacobi operators ; global convergence ; generalized eigenvalue problem ; Cholesky-Jacobi method
Sažetak
In this paper we prove the global convergence of the complex Jacobi method for Hermitian matrices for a large class of generalized serial pivot strategies. For a given Hermitian matrix $A$ of order $n$ we find a constant $\gamma<1$ depending on $n$, such that $S(A′)\leq\gamma S(A)$, where $A′$ is obtained from $A$ by applying one or more cycles of the Jacobi method and $S(.)$ stands for the off-norm. Using the theory of complex Jacobi operators, the result is generalized so it can be used for proving convergence of more general Jacobi-type processes. In particular, we use it to prove the global convergence of Cholesky-Jacobi method for solving the positive definite generalized eigenvalue problem.
Izvorni jezik
Engleski
Znanstvena područja
Matematika
POVEZANOST RADA
Projekti:
HRZZ-IP-2014-09-3670 - Matične faktorizacije i blok dijagonalizacijski algoritmi (MFBDA) (Hari, Vjeran, HRZZ - 2014-09) ( CroRIS)
Ustanove:
Prirodoslovno-matematički fakultet, Zagreb,
Fakultet kemijskog inženjerstva i tehnologije, Zagreb
Citiraj ovu publikaciju:
Časopis indeksira:
- Current Contents Connect (CCC)
- Web of Science Core Collection (WoSCC)
- Science Citation Index Expanded (SCI-EXP)
- SCI-EXP, SSCI i/ili A&HCI
- Scopus
