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.

Key words: neutron transport equation, Gerschgorin disk criterion, perturbation analysis, Rayleigh quotient iteration