IKKI QATLAMLI ITERATSION SXEMALAR VA ULARNING CHIZIQLI OPERATOR MASALALARIDA AMALIY TATBIQI

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Выпуск: Том 3 № 59 : Наука и инновация
Раздел: Статьи
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FarDU amaliy matematika mutaxassisligi magistranti
info@in-academy.uz

Аннотация:

Ushbu maqolada ikki qatlamli iteratsion sxemalar nazariyasi va ularning chiziqli operator masalalarida amaliy tatbiqi ko‘rib chiqiladi. Masalalar Hilbert fazosida aniqlangan chiziqli operatorlar shaklida ifodalanadi. Ikki qatlamli sxemalarning barqarorligi, konvergentsiyasi va amaliy samaradorligi tahlil qilinadi. Preconditionerlar yordamida iteratsion jarayonning tezlashtirilishi va yechim sifatining oshirilishi batafsil ko‘rsatib beriladi. Amalga oshirilgan hisoblashlar sxemaning an’anaviy Jacobi va Gauss-Seidel usullariga nisbatan sezilarli afzalliklarini tasdiqlaydi.

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Tuychiyeva, D. . (2025). IKKI QATLAMLI ITERATSION SXEMALAR VA ULARNING CHIZIQLI OPERATOR MASALALARIDA AMALIY TATBIQI. Наука и инновация, 3(59), 158–160. извлечено от https://www.in-academy.uz/index.php/si/article/view/69815

Библиографические ссылки:

Saad, M., & Elman, H. (2010). Iterative Methods for Sparse Linear Systems. SIAM.

Golub, G. H., & Van Loan, C. F. (2013). Matrix Computations. 4th Edition, Johns Hopkins University Press.

Hackbusch, W. (1994). Iterative Solution of Large Sparse Systems of Equations. Springer-Verlag.

Axelsson, O. (1996). Iterative Solution Methods. Cambridge University Press.

Ortega, J. M., & Rheinboldt, W. C. (1970). Iterative Solution of Nonlinear Equations in Several Variables. Academic Press.

Varga, R. S. (2000). Matrix Iterative Analysis. Springer-Verlag.