Vejdi I. Hasanov

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Some semi-discrete analogous of well known one-point family of iterative methods for solving nonlinear scalar equations dependent on an arbitrary constant are proposed. The new families give multi-point iterative processes with the same or higher order of convergence. The convergence analysis and numerical examples are presented.
The two matrix iterations Xk+1 = I ∓ A∗X−1 k A are known to converge linearly to a positive definite solution of the matrix equations X ± A∗X−1A = I, respectively, for known choices of X0 and under certain restrictions on A. The convergence for previously suggested starting matrices X0 is generally very slow. This paper explores different initial choices of(More)
In this paper we consider the positive definite solutions of nonlinear matrix equation X + A X−δA = Q, where δ ∈ (0, 1], which appears for the first time in [S.M. El-Sayed, A.C.M. Ran, On an iteration methods for solving a class of nonlinear matrix equations, SIAM J. Matrix Anal. Appl. 23 (2001) 632–645]. The necessary and sufficient conditions for the(More)
where F is a Fréchet-differentiable operator defined on an open subset D of a Banach space X with values in a Banach space Y . Finding roots of Eq.(1) is a classical problem arising in many areas of applied mathematics and engineering. In this study we are concerned with the problem of approximating a locally unique solution α of Eq.(1). Some of the well(More)
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