On four-layer iterative scheme

Abstract

The work objective is to study the four-layer scheme convergence rate. The problem of finding an approximate solution to the linear operator equation Au = f is considered. Two-layer and three-layer iterative methods are used to solve this problem. At that, the three-layer conjugate directions methods converge faster than the two-layer gradient methods. The research problem is to establish whether the four-layer scheme has a speed advantage as compared to the three-layer scheme. The four-layer scheme is constructed, and its parameters are calculated for this purpose. It is proved that the four-layer iterative scheme of a variational type for solving finite-difference equations downs to the three-layer scheme.

Keywords

• сеточные уравнения
• трехслойная схема
• четырехслойная схема
• методы вариационного типа
• finite-difference equations
• three-layer scheme
• four-layer scheme
• variational methods