Solving fixed point equation by niche particle swarm optimization

Solving fixed point equation by traditional iterative algorithm not only has the very big relation with the initial point but also cannot satisfy parallel. In this paper, a niche particle swarm optimization is used to solve fixed point equation, which sufficiently exerted the advantage of particle swarm optimization such as group search, strong robustness and it satisfies the question of parallel solving fixed point equation in engineering and needn´t to verify the conditions of Banach theorem. It overcomes the influence of the initial point. Several numerical simulation results show that the algorithm offers an effective way to solve fixed point equation, high convergence rate, high accuracy and robustness.