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Volume 24, Issue 5
Modified Newton's Algorithm for Computing the Group Inverses of Singular Toeplitz Matrices

Jian-feng Cai, Michael K. Ng & Yi-min Wei

J. Comp. Math., 24 (2006), pp. 647-656.

Published online: 2006-10

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  • Abstract

Newton's iteration is modified for the computation of the group inverses of singular Toeplitz matrices. At each iteration, the iteration matrix is approximated by a matrix with a low displacement rank. Because of the displacement structure of the iteration matrix, the matrix-vector multiplication involved in Newton's iteration can be done efficiently. We show that the convergence of the modified Newton iteration is still very fast. Numerical results are presented to demonstrate the fast convergence of the proposed method.

  • Keywords

Newton's iteration, Group inverse, Toeplitz matrix, Displacement rank.

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COPYRIGHT: © Global Science Press

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@Article{JCM-24-647, author = {Jian-feng Cai, Michael K. Ng and Yi-min Wei}, title = {Modified Newton's Algorithm for Computing the Group Inverses of Singular Toeplitz Matrices}, journal = {Journal of Computational Mathematics}, year = {2006}, volume = {24}, number = {5}, pages = {647--656}, abstract = {

Newton's iteration is modified for the computation of the group inverses of singular Toeplitz matrices. At each iteration, the iteration matrix is approximated by a matrix with a low displacement rank. Because of the displacement structure of the iteration matrix, the matrix-vector multiplication involved in Newton's iteration can be done efficiently. We show that the convergence of the modified Newton iteration is still very fast. Numerical results are presented to demonstrate the fast convergence of the proposed method.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8780.html} }
TY - JOUR T1 - Modified Newton's Algorithm for Computing the Group Inverses of Singular Toeplitz Matrices AU - Jian-feng Cai, Michael K. Ng & Yi-min Wei JO - Journal of Computational Mathematics VL - 5 SP - 647 EP - 656 PY - 2006 DA - 2006/10 SN - 24 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8780.html KW - Newton's iteration, Group inverse, Toeplitz matrix, Displacement rank. AB -

Newton's iteration is modified for the computation of the group inverses of singular Toeplitz matrices. At each iteration, the iteration matrix is approximated by a matrix with a low displacement rank. Because of the displacement structure of the iteration matrix, the matrix-vector multiplication involved in Newton's iteration can be done efficiently. We show that the convergence of the modified Newton iteration is still very fast. Numerical results are presented to demonstrate the fast convergence of the proposed method.

Jian-feng Cai, Michael K. Ng and Yi-min Wei. (2006). Modified Newton's Algorithm for Computing the Group Inverses of Singular Toeplitz Matrices. Journal of Computational Mathematics. 24 (5). 647-656. doi:
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