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对称Toeplitz线性方程组的基于余弦变换的最佳预优矩阵 被引量：1

COSINE TRANSFORM BASED PRECONDITIONER FOR SYMMETRIC TOEPLITZ SYSTEMS
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摘要 利用第四类离散余弦变换矩阵构造出求解对称Toeplitz线性方程组的最佳预优矩阵,构造该预优矩阵所需的运算量为O(n).理论和数值实验显示,利用本文中所构造的预优矩阵求解对称Toeplitz线性方程组所需的迭代次数与现有的其它类型预优矩阵差不多,但预优矩阵的构造要更简单. Based on the forth discrete Cosine transform, a new optimal preconditioner for sym- metric Toeplitz systems was constructed, and the operations for the construction of the new preconditioner is O（n）. As the theoretical analysis and numerical experiments show, the convergent behavior is similar to the other preconditioners, but the construction of the new preconditioner is simpler.
作者 汪祥 李乐波
机构地区 南昌大学理学院数学系
出处 《数值计算与计算机应用》 CSCD 北大核心 2010年第3期223-231,共9页 Journal on Numerical Methods and Computer Applications
基金 江西省自然科学基金(2007GQS2063) 江西省教育厅青年科学基金(GJJ09450) 中国科学院科学与工程计算国家重点实验室资助
关键词 TOEPLITZ矩阵 预条件共轭梯度法(PCG) 第四类离散余弦变换矩阵(DCT-IV) Toeplitz matrices preconditioned conjugate gradient （PCG） discrete cosinetransform IV
分类号 O241.6 [理学—计算数学]
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参考文献13

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同被引文献11

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数值计算与计算机应用
2010年 第3期

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