The applications of the generalized norm solver show promising results in our two sample problems. The line-fitting problem shows that our solver can correctly remove spikes and noise added to the data. The 1-D Galilee problem shows that the solver can properly produce a blocky model space while removing outliers. In terms of convergence, the hybrid solver takes longer to converge than the Huber solver. While only the one-dimensional problem is examined with this solver, we plan to further explore this solver with 2-D field data problem and directly compare the result with the IRLS algorithm.