Volume 19, Issue 2
Sine Transform Matrix for Solving Toeplitz Matrix Problems

Li Zhi Cheng

J. Comp. Math., 19 (2001), pp. 167-176

Published online: 2001-04

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  • Abstract

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 presented.

  • Keywords

Preconditioner Toeplitz systems The fast sine transform Conjugate gradient algorithm

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COPYRIGHT: © Global Science Press

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@Article{JCM-19-167, author = {}, title = {Sine Transform Matrix for Solving Toeplitz Matrix Problems}, journal = {Journal of Computational Mathematics}, year = {2001}, volume = {19}, number = {2}, pages = {167--176}, abstract = { 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 presented. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8969.html} }
TY - JOUR T1 - Sine Transform Matrix for Solving Toeplitz Matrix Problems JO - Journal of Computational Mathematics VL - 2 SP - 167 EP - 176 PY - 2001 DA - 2001/04 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8969.html KW - Preconditioner KW - Toeplitz systems KW - The fast sine transform KW - Conjugate gradient algorithm AB - 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 presented.
Li Zhi Cheng. (1970). Sine Transform Matrix for Solving Toeplitz Matrix Problems. Journal of Computational Mathematics. 19 (2). 167-176. doi:
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