求解鞍点问题的多项式加速超松弛方法

摘要

为了快速有效地求解大型稀疏鞍点问题,在广义逐次超松弛(GSOR)迭代算法的基础上,结合Chebyshev多项式加速技术,本文构造了一种多项式加速超松弛迭代算法,并研究了该算法的收敛性.通过讨论加速后迭代矩阵的收敛性证明了新方法比加速前的迭代法具有快的收敛速度.数值例子也表明新方法提高了GSOR算法的收敛效率.%In order to solve large sparse saddle point problems (SPP) quickly and efficiently, we construct in this paper a polynomial accelerative iterative algorithm through accelerating the generalized SOR (GSOR) iterative algorithm and using the Chebyshev polynomial. The convergence of the algorithm is also studied. Meanwhile, by examining the convergence of accelerated iterative matrix, the result shows that the new method converges faster than the GSOR method. Numerical results further demonstrate that the new method is more efficient than the GSOR method.