该文针对现有椭圆球面波函数(PSWFs)求解算法存在的效率低、硬件实现复杂度高,尤其是精度不可控的问题,结合线性时变系统理论,提出一种基于微分方程状态转移矩阵逼近的PSWFs求解方法.该算法通过求解小区间上的状态转移矩阵来逼近整个时间区间上的状态转移矩阵,进而求得离散时间点上的系统运动轨迹,即PSWFs数值解.理论推导了求解误差并修正了算法,修正后算法具有简明的误差表达式,与Parr算法和Legendre多项式逼近算法在求解精度和复杂度上进行了对照分析.结果表明,该文算法求解精度高且可控,时间和空间复杂度低,易于硬件实现.%The existing algorithms for Prolate Spheroidal Wave Functions (PSWFs) have poor efficiency, high complexity in hardware implementation and especially uncontrollable precision. To overcome the above weaknesses, a new algorithm based on state transition matrix approximation of differential equation is proposed combining the theory of linear time-varying system. In the new algorithm, the state transition matrix on the whole interval is approximated by the ones on very small intervals. After that, the movement track of the system on discrete time spot is attained, and that is the numerical solution of PSWFs. The expression of error to the precise value is deduced theoretically and then the algorithm is improved to get the briefer error expression. The new algorithm is compared and analyzed with the one proposed by Parr and the approximation algorithm of Legendre polynomials on the calculation precision and complexity. The simulation results show that the proposed algorithm has high and controllable precision, low complexity and are easy for hardware implementation.
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