Homotopy Understanding of Iterative Methods

Preconditioned Iterative Methods for Homotopy Curve Tracking

Homotopy algorithms are a class of methods for solving systems of nonlinear equations that are globally convergent with probability one. All homotopy algorithms are based on the construction of an appropriate homotopy map and then the tracking of a curve in the zero set of this homotopy map. The fundamental linear algebra step in these algorithms is the computation of the kernel of the homotopy...

Iterative Methods for Nonlinear Equations Using Homotopy Perturbation Technique

In this paper, we suggest and analyze some iterative methods for solving nonlinear equations using the homotopy perturbation technique coupled with system of equations. In addition, we show that the homotopy polynomial is exactly the the Adomian polynomial and this establishes the equivalence between the homotopy perturbation and decomposition techniques. Our method of establishing the equivale...

Weights in block iterative methods

In this paper we introduce a sequential block iterative method and its simultaneous version with op-timal combination of weights (instead of convex combination) for solving convex feasibility problems.When the intersection of the given family of convex sets is nonempty, it is shown that any sequencegenerated by the given algorithms converges to a feasible point. Additionally for linear feasibil...

Numerical Solution of Sawada-Kotera equation by using Iterative Methods

Phase Only Synthesis of Antenna Patterns Using Iterative Restoration Methods

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...