Computing Moore-Penrose inverses of Toeplitz matrices by Newton's iteration
نویسندگان
چکیده
We modify the algorithm of [1], based on Newton’s iteration and on the concept of 2-displacement rank, to the computation of the Moore-Penrose inverse of a rank-deficient Toeplitz matrix. Numerical results are presented to illustrate the effectiveness of the method.
منابع مشابه
The reverse order law for Moore-Penrose inverses of operators on Hilbert C*-modules
Suppose $T$ and $S$ are Moore-Penrose invertible operators betweenHilbert C*-module. Some necessary and sufficient conditions are given for thereverse order law $(TS)^{ dag} =S^{ dag} T^{ dag}$ to hold.In particular, we show that the equality holds if and only if $Ran(T^{*}TS) subseteq Ran(S)$ and $Ran(SS^{*}T^{*}) subseteq Ran(T^{*}),$ which was studied first by Greville [{it SIAM Rev. 8 (1966...
متن کاملModified Newton’s Algorithm for Computing the Group Inverses of Singular Toeplitz Matrices
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 modifie...
متن کاملA Homotopic/Factorization Process for Toeplitz-like Matrices with Newton’s/Conjugate Gradient Stages
We modify our earlier homotopic process for iterative inversion of Toeplitz and Toeplitz-like matrices to improve the choice of the initial approximate inverses at every homotopic step. This enables us to control the condition of the auxiliary matrices and to accelerate convergence substantially. The algorithm extends our older approach where the input matrix was factorized into the product of ...
متن کاملComputing generalized inverses using LU factorization of matrix product
An algorithm for computing {2, 3}, {2, 4}, {1, 2, 3}, {1, 2, 4}-inverses and the Moore-Penrose inverse of a given rational matrix A is established. Classes A{2, 3}s and A{2, 4}s are characterized in terms of matrix products (R∗A)†R∗ and T ∗(AT ∗)†, where R and T are rational matrices with appropriate dimensions and corresponding rank. The proposed algorithm is based on these general representat...
متن کاملRank Equalities Related to Generalized Inverses of Matrices and Their Applications
This paper is divided into two parts. In the first part, we develop a general method for expressing ranks of matrix expressions that involve Moore-Penrose inverses, group inverses, Drazin inverses, as well as weighted Moore-Penrose inverses of matrices. Through this method we establish a variety of valuable rank equalities related to generalized inverses of matrices mentioned above. Using them,...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Mathematical and Computer Modelling
دوره 40 شماره
صفحات -
تاریخ انتشار 2004