Naslov
On the Global and Cubic Convergence of a Quasi-Cyclic Jacobi Method

Autori
Rhee, H., Noah ; Hari, Vjeran

Izvornik
Numerische Mathematik (0029-599X) 66 (1993); 97-122

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Symmetric matrix; quasi-cyclic Jacobi method; cubic convergence

Sažetak
In this paper we consider the global and the cubic convergence of a quasi-cyclic Jacobi method for the symmetric eigenvalue problem. The method belongs to a class of quasi-cyclic methods recently proposed by W. Mascarenhas. Mascarenhas showed that the methods from his class asymptotically converge cubically per quasi-sweep (one quasi-sweep is equivalent to 1.25 cyclic sweeps) provided the eigenvalues are simple . Here we prove the global convergence of our method and derive very sharp asymptotic convergence bounds in the general case of multiple eigenvalues. We discuss the ultimate cubic convergence of the method and present several numerical examples which well comply with the theory.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA