A NEW APPROACH TO SOLVE SYSTEMS OF LINEAR EQUATIONS

• 来源期刊: 计算数学（英文版）
• 学科: 数学
• 关键词: Iterative method Linear systems Classical dynamics.
• 年，卷（期）: 2001,（4）
• 页码范围: 445-448
• 页数: 4页
• 分类号: O1
• 语种: 英文

摘要

We propose a new iterative approach to solve systems of linear equations. The new strategy integrates the algebraic basis of the problem with elements from classical mechanics and the finite difference method. The approach defines two families of convergent iterative methods. Each family is characterized by a linear differential equation, and every method is obtained from a suitable finite difference scheme to integrate the associated differential equation. The methods are general and depend on neither the matrix dimension nor the matrix structure. In this preliminary work, we present the basic features of the method with a simple application to a low dimensional system.