Schur algorithm combined with an extrapolation method for inverse scattering problems

Abstract

We propose schur algorithm combined with an extrapolation method for inverse scattering problems in the coarse discretization environment. The proposed method compensates the discretization error to two decimal digits for 3 stages extrapolation. The schur algorithm can be interpreted as the initial value problem of one step scheme for solving the coupled-mode differential equation which has no closed from solutions. There is no appropriate way to improve the performance of schur algorithm without decreasing mesh size. In order to apply the extrapolation scheme, we analyze the discretization error behavior, derive the error bound and obtain the asymptotic expansion of the schur recursion formula. For robustness, we proposed stable estimation scheme for multistep coupling coefficients. The iterative extrapolation scheme is used to minimize the estimation error. As shown in simulation results, the proposed method compensates the global discretization error and make the computed coupling coefficients converge to exact coupling profile.