【摘要】 中子输运方程源项反演问题中,有效倍增因子的求解经过球谐函数展开和差分离散后,转化为求解大型矩阵的特征值问题.针对矩阵的特点,利用Gerschgorin圆盘定理,给出反幂法迭代初值的选取方法,并进行相应的扰动分析.针对有效倍增因子是矩阵最大特征值的特点,采用瑞利商迭代算法进行求解.理论和算例表明,该方法不需选取特定初值,达到三阶收敛速度.更多还原

【Abstract】 With spherical harmonic function expansion and finite difference discretization,an inversion problem of neutron transport equation is turned to solving effective multiplication factor related to eigenvalue problem.According to characteristics of the matrix,Gerschgorin disk theorem is applied to initial value selection without any physical experience.Rayleigh quotient iteration algorithm is used in solving effective multiplication factor.Third order convergence is achieved without a specific initial value.更多还原