Hi Yi,
There are two basic methods for solving for the tensor in our software, the linear and non-linear methods. The non-linear methods includes three choices for optimization for the search for the lowest cost positive definite solution, Gradient Descent, Powell NEWUOA and Hybrid. The Powell method gives the lowest cost, but is slower than the gradient search. The hybrid method is the default method and combines the two using the Powell method at the usually relatively few voxels that are highly anisotropic. Usually these points are at a relatively few very noisy voxels.
Daniel