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The generalized inverse A T ,S of a matrix A is a {2}-inverse of A with the prescribed range T and null space S. A representation for the generalized inverse A T ,S has been recently developed with the condition σ(GA|T ) ⊂ (0,∞), where G is a matrix with R(G) = T and N(G) = S. In this note, we remove the above condition. Three types of iterative methods for(More)
A constructive perturbation bound of the Drazin inverse of a square matrix is derived using a technique proposed by G. Stewart and based on perturbation theory for invariant subspaces. This is an improvement of the result published by the authors Wei and Li [Numer. Linear Algebra Appl., 10 (2003), pp. 563–575]. It is a totally new approach to developing(More)
Let C(r) = [Cij ], r = 1, 2, . . . , R, be block m×m matrices where Cij (r) are nonnegative Ni ×Nj matrices for i, j = 1, 2, . . . , m. Let ‖ · ‖ be a consistent matrix norm. Denote for each r by B(r) = [‖Cij (r)‖] an m×m matrix. The relation of the spectral radii ρ( ∏R r=1 C(r)) and ρ( ∏R r=1 B(r)) is studied in this paper. It is shown with two proofs that(More)
Perturbation bounds for the relative error in the eigenvalues of diagonalizable and singular matrices are derived by using perturbation theory for simple invariant subspaces of a matrix and the group inverse of a matrix. These upper bounds are supplements to the related perturbation bounds for the eigenvalues of diagonalizable and nonsingular matrices. ©(More)
Given a square matrix A and its perturbation matrix E, a new expression for the Drazin inverse B of B 1⁄4 Aþ E is derived if AAB 1⁄4 ðAADBÞ or BAA 1⁄4 ðBAADÞ. Based on the new expression, a bound of the relative error of B is developed. Some known results in the literature on the Drazin inverse and the perturbation bound are included by this new formula as(More)
Discrete tomography deals with image reconstruction of an object with finitely many gray levels (such as two). Different approaches are used to model the raw detector reading. The most popular models are line projection with a lattice of points and strip projection with a lattice of pixels/cells. The line-based projection model fits some applications but(More)