SINE TRANSFORM MATRIX FOR SOLVING TOEPLITZ MATRIX PROBLEMS

• 作者: Li-zhi Cheng
• 来源期刊: 计算数学（英文版）
• 学科: 数学
• 关键词: Preconditioner Toeplitz systems The fast sine transform Conjugate gradient
• 年，卷（期）: 2001,（2）
• 页码范围: 167-176
• 页数: 10页
• 分类号: O1
• 语种: 英文

摘要

In recent papers, some authors studied the solutions of symmetricpositive definite(SPD) Toeplitz systems Tn x = b by the conjugate gradient method(CG) with different sine trans- forms based preconditioners. In this paper, we first discuss the properties of eigenvalues for the main known circulant, skew circulant and sine transform based preconditioners. A counter example shows that E.Boman's preconditioner is only positive semi-definite for the banded Toeplitz matrix. To use preconditioner effectively, then we propose a modified Boman's preconditioner and a new Cesaro sum type sine transform based preconditioner. Finally, the results of numerical experimentation with these two preconditioners are pre- sented.