Optimum spectral parameter and convergency for stationary iterative methods in the case of three-diagonal SLAE
Yükleniyor...
Dosyalar
Tarih
2003
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Selcuk University Research Center of Applied Mathematics
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
The modified stationary iterative methods of the solution of system of the linear algebraic equations (SLAE) are considered.For SLAE with a three-diagonal matrix with constant factors it is shown, that eigenvalues of modified matrices or the operator, participating in series of simple iteration, are expressed through roots of Chebyshev polynomials of the second kind. On this basis strict expressions through factors of an initial matrix for optimum parameter of convergence and spectral radius are found. So for Successive Overrelaxation method strict expression for the optimum parameter of convergence w0 laying on an interval (0,2) is found. It is shown, that convergence of the optimum modified series essentially improves.
Açıklama
url: http://sjam.selcuk.edu.tr/sjam/article/view/129
Anahtar Kelimeler
Sabit yinelemeli yöntemler, Spektral yarıçap, Matris denklemleri, Stationary iterative methods, Spectral radius, Matrix equations
Kaynak
Selcuk Journal of Applied Mathematics
WoS Q Değeri
Scopus Q Değeri
Cilt
4
Sayı
Künye
Kulikov, S. (2003). Optimum spectral parameter and convergency for stationary iterative methods in the case of three-diagonal SLAE. Selcuk Journal of Applied Mathematics, 4 (2), 89-102.
