The multigrid method is compared to ICCG/MICCG methods for solving symmetric systems of linear equations arising from approximations to differential equations with jump discontinuities in the coefficients. An optimal multigrid algorithm for these types of problems is developed. It includes pattern relaxation and acceleration. Optimization of ICCG/MICCG algorithms is investigated. This includes the effect of adding extra (up to ten) bands to the approximate factorization and of different grid ordering schemes. Numerical results are presented comparing the scalar work of the algorithms. For large problems the multigrid algorithm is superior. The optimal multigrid scheme can be highly vectorized.