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广义块Toeplitz特征值问题的基于sine变换的预处理子
  • ISSN号：1006-6837
  • 期刊名称：《数学研究》
  • 时间：0
  • 分类：O151[理学—数学;理学—基础数学]
  • 作者机构：[1]厦门大学数学科学学院,福建厦门361005
  • 相关基金：The work of the author is supported by National Natural Science Foundation of China Nos 10531080
作者： 王元媛[1], 卢琳璋[1]
关键词： 分块Toeplitz矩阵, 双对称, sine变换, 预处理Lanczos方法, block Toeplitz matrix, quadrantally symmetric, sine transform, preconditioned Lanczos method
中文摘要：

在求块Toeplitz矩阵束（Amn，Bmn）特征值的Lanczos过程中，通过对移位块Toepltz矩阵Amn-ρBmn进行基于sine变换的块预处理，从而改进了位移块Toeplitz矩阵的谱分布，加速了Lanczos过程的收敛速度．该块预处理方法能通过快速算法有效快速执行．本文证明了预处理后Lanczos过程收敛迅速，并通过实验证明该算法求解大规模矩阵问题尤其有效．

英文摘要：

We employ the block sine transform-based preconditioner to precondition the shifted block Toeplitz matrix Amn - ρBmn involved in the Lanczes method to compute the minimum eigenvalue of the generalized block Toeplitz eigenvalue problem Anmx=λBmnx, where Amn, and Bmn are partitioned into m×m blocks with order n. The block sine transform-based preconditioner can improve the spectral distribution of the shifted block Toeplitz matrix and, hence, can speed up the convergence rate of the preconditioned Lanczos method. The block sine transform-based preconditioner can be implemented efficiently by the fast transform algorithm. A convergence analysis shows that the preconditioned Lanczos method converges sufficiently fast, and numerical results show that this method is highly effective for large matrix.

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期刊信息
  • 《数学研究》
  • 主管单位:厦门大学
  • 主办单位:厦门大学数学科学学院 福建省数学会
  • 主编：林群
  • 地址：厦门大学数学系
  • 邮编：361005
  • 邮箱：jmaths@xmu.edu.cn
  • 电话：0592-2580752 21828321
  • 国际标准刊号：ISSN：1006-6837
  • 国内统一刊号：ISSN：35-1177/O1
  • 邮发代号:
  • 获奖情况:
  • 国内外数据库收录:
  • 美国数学评论（网络版）,德国数学文摘
  • 被引量:1284