TY - JOUR
T1 - Modified Newton's Algorithm for Computing the Group Inverses of Singular Toeplitz Matrices
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 - <p style="text-align: justify;">Newton&#39;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&#39;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.</p>