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- Gyurhan H. Nedzhibov, Vejdi I. Hasanov, Milko G. Petkov
- Numerical Algorithms
- 2006

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.

- Ivan G. Ivanov, Vejdi I. Hasanov, Frank Uhlig
- Math. Comput.
- 2005

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)

- Vejdi I. Hasanov, Ivan G. Ivanov
- Applied Mathematics and Computation
- 2005

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)

- Vejdi I. Hasanov
- Applied Mathematics and Computation
- 2010

- Vejdi I. Hasanov, Ivan G. Ivanov
- Applied Mathematics and Computation
- 2004

- Vejdi I. Hasanov, Sevdzhan Hakkaev
- Computers & Mathematics with Applications
- 2016

The two matrix equations X + A∗X−2A = I and X −A∗X−2A = I are studied. We construct iterative methods for obtaining positive definite solutions of these equations. Sufficient conditions for the existence of two different solutions of the equation X + A∗X−2A = I are derived. Sufficient conditions for the existence of positive definite solutions of 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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