Modified Fisher scoring algorithms using Jacobi or Gauss-Seidel subiterations

In a parameter estimation problem with large numbers of unknown parameters, traditional algorithms such as Fisher scoring and Newton-Raphson become impractical. A typical case is solution by discretization of linear inverse problems; an example is medical image reconstruction from projections. This article introduces a modification to the Fisher scoring method. Instead of solving the linear system of equations of each Fisher scoring iteration exactly, the solution of these equations is approximated by using the Jacobi or Gauss-Seidel scheme. Simulation studies show that these modified al-gorithms, especially the one with Gauss-Seidel scheme, exhibit much faster convergence than competitors such as the EM algorithm.