ITERATIONS FOR APPROXIMATING LIMIT REPRESENTATIONS OF GENERALIZED INVERSES

Our underlying motivation is the iterative method for the implementation of the limit representation of the Moore-Penrose inverse$\lim\limits _{\alpha \to 0} \left( \alpha I+A^*A\right) ^{-1} A^*$ from [\v Zukovski, Lipcer, On recurent computation of normal solutions of linear algebraic equations, \v Z. Vicisl. Mat. i Mat. Fiz. 12 (1972), 843--857] and[\v Zukovski, Lipcer, On computation pseudoinverse matrices, \v Z. Vicisl. Mat. i Mat. Fiz. 15 (1975), 489--492].  The iterative process for the implementation of the general limit formula$\lim\limits _{\alpha \to 0}(\alpha I+R^*S) ^{-1}R^*$was defined in [P.S. Stanimirovi\'c, Limit representations of generalized inverses and related methods, Appl. Math. Comput. 103 (1999), 51--68].In this paper we develop an improvement of this iterative process.The iterative method defined in such a way is able to produce the result in a predefined number of iterative steps. Convergence properties of defined iterations are further investigated

A Note on Computing the Generalized Inverse A^(2)_{T,S} of a Matrix A

The generalized inverse A T,S (2) 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 (2) has been recently developed with the condition σ (GA| T)⊂(0,∞), where G is a matrix with R(G)=T andN(G)=S. In this note, we remove the above condition. Three types of iterative methods for A T,S (2) are presented if σ(GA|T) is a subset of the open right half-plane and they are extensions of existing computational procedures of A T,S (2), including special cases such as the weighted Moore-Penrose inverse A M,N † and the Drazin inverse AD. Numerical examples are given to illustrate our results

Symbolic computation of Hankel determinants and matrix generalized inverses

In this thesis, existing methods for symbolic computation of Hankel deteriminants and matrix generalized inverses are modified and new are introducted. There are derived closed-form expressions for Hankel determinants of different classes of sequences. It is constructed the method for rapid computation of generalized inverses whose complexity reaches theoretical lower bound. There are also constructed new methods for computation of generalized inverses of rational and polynomial matrices