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Our underlying motivation is the iterative method for the implementation of the limit representation of the Moore-Penrose inverse lim αI0 (αI + A*A)-1 A* from [Žukovski, Lipcer, On recurent computation of normal solutions of linear algebraic equations, Ž. Vicisl. Mat. i Mat. Fiz. 12 (1972), 843-857] and [Žukovski, Lipcer, On computation pseudoinverse matrices, Ž. Vicisl. Mat. i Mat. Fiz. 15 (1975), 489-492]. The iterative process for the implementation of the general limit formula lim αI0 (αI + R*S)-1R* was defined in [P.S. Stanimirović, Limit representations of gen- eralized 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. [ABSTRACT FROM AUTHOR]

In this paper, a finite filter is used in the structure of the Barzilai–Browein (BB) gradient method in order to propose a new modified BB algorithm for solving large-scale unconstrained optimization problems. Our algorithm is equipped with a relaxed nonmonotone line search technique which allows the algorithm to enjoy the nonmonotonicity properties from scratch. Under some suitable conditions, the global convergence property of the new proposed algorithm is established. Numerical results on some test problems in CUTEr library show the efficiency and effectiveness of the new algorithm in practice too. [ABSTRACT FROM PUBLISHER]

In this paper we analyse the Kaczmarz projection algorithm with remotest set control of projection indices. According to this procedure, at each iteration the projection index is one which gives the maximal absolute value of the corresponding residual. We prove that for under-determined full row rank systems and under some assumptions valid for problems arising in algebraic reconstruction of images in computerized tomography, this selection procedure has the property that each row index is selected at least once during the Kaczmarz algorithm iterations. [ABSTRACT FROM AUTHOR]