Conjugate gradient method may suffer convergent issue for matrices with large condition number. Jacobi preconditioner, adopted in this kernel, is widely used and dramatically reduces the overall number of iterations to solve the linear system. For some matrices, however, the solver with Jacobi preconditioner is not able to converge. For instance, the number of iterations for some matrices in the above table reached the upper limit 5000 with the preset relative tolerance 10e-12.
Although the solver, for some other matrices e.g. ted_B_unscaled, meets the preset tolerance within the preset number of iteration limit, there might still be some mismatches in the result vector compared to the golden reference x. The solution to this issue is to further reduce the tolerance value to such as 10e-15.