BICGSTAB算法在波前重构和控制中的应用

自适应光学波前重构和控制对精度和实时性的要求很高。BICGSTAB算法可用于非正定对称的线性系统方程的求解,并且速度快、精度高,稳定性好。基于Fried网格,提出将BICGSTAB算法引入自适应光学波前重构和控制系统方程的求解,并与SVD以及几种常见的迭代算法(Jacobi,Seidel,SOR以及SSOR)作比较。仿真结果表明,对于121阶系统,BICGSTAB法达到0.01%精度仅仅需要不到70次的迭代;SVD法达到0.01%需要近300次;四种常见迭代方法即使104次也没有收敛。这说明BICGSTAB具有更高的速度和精度,能够更好地满足自适应光学系统实时性和精度的需要。

Application of BICGSTAB algorithm in wave-front reconstruction and control

The precise and real-time character requirement is very important for wavefront reconstruction and control in an adaptive optical system. The BICGSTAB algorithm could be used to solve nonsymmetrical or non-positive system linear equations, with advantages of high speed, high precision and stability. Based on Fried grids, BICGSTAB method is applied to adaptive optical wavefront reconstruction and control, and compared with SVD four common iteration methods (Jacobi, seidel, SOR, SSOR). Simulation shows that for 121-dim system the BICGSTAB method only needs less than 70 iterations to get 0.01% relative error while SVD does about 300 iterations, the other four methods do not converge even with 104iterations, so the BICGSTAB method is of higher precision and more efficiency, and does better to meat the requirement of adaptive optical system for precision and real-time operation.