The convergence features of a preconditioned algorithm for the convection-diffusion equation based on its diffusion part are considered. An analysis of the distribution of the eigenvalues of the preconditioned matrix and of the fundamental parameters of convergence are provided, showing the existence of a proper cluster of eigenvalues and the superlinear behavior of preconditioned iterations. T...

‎In this paper‎, ‎an accelerated gradient based iterative algorithm for solving systems of coupled generalized Sylvester-transpose matrix equations is proposed‎. ‎The convergence analysis of the algorithm is investigated‎. ‎We show that the proposed algorithm converges to the exact solution for any initial value under certain assumptions‎. ‎Finally‎, ‎some numerical examples are given to demons...

In this work, the method of iterative Fourier transform phase reconstruction, conventionally used in holography and optical image reconstruction, is applied to phase only synthesis of antenna patterns. The method is applied to two types of pattern synthesis problems: "main lobe beam shaping" and "side-lobe-level reduction". The proposed method is most useful in the efficient employment of attai...

Several preconditioners are proposed for improving the convergence rate of the iterative method derived from splitting. In this paper, the comparison theorem of preconditioned iterative method for regular splitting is proved. And the convergence and comparison theorem for any preconditioner are indicated. This comparison theorem indicates the possibility of finding new preconditioner and splitt...

We study generalized equations of the following form: 0 ∈ f(x) + g(x) + F (x) (∗); where f is Fréchet differentiable in a neighborhood of a solution x∗ of (*) and g is Fréchet differentiable at x∗ and where F is a set-valued map acting in Banach spaces. We prove the existence of a sequence (xk) satisfying 0 ∈ f(xk) + g(xk) + ( ∇f(xk) + [xk−1, xk; g] ) (xk+1− xk) + F (xk+1) which is super-linear...

The purpose of this paper is to provide the convergence theory for the iterative approach given by Chu [SIAM J. Numer. Anal.,29 (1992), pp. 885–903] in the context of solving inverse singular value problems. We give a detailed convergence analysis and investigate the ultimate rate of convergence. Numerical results which confirm our theory are presented.