Modified Newton'S Algorithm For Computing The Group Inverses Of Singular Toeplitz Matrices.
Jian-feng Cai 1, Michael K. Ng 2, Yi-min Wei 31 Department of Mathematics, The Chinese University of Hong Kong, Hong Kong
2 Department of Mathematics, Hong Kong Baptist University, Hong Kong
3 School of Mathematical Sciences, Fudan University, Shanghai 200433, China; Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University), Ministry of Education
Received 2005-1-12 Revised 2006-3-20 Online 2006-9-14 Accepted
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.
Key words: Newton's iteration; Group inverse; Toeplitz matrix; Displacement rank.