This paper proposes two unconstrained algorithms, the Steepest Decent (SD) algorithm and the Conjugate Gradient (CG) algorithm, based on a superexcellent cost function [1～3]. At the same time, two constrained algorithms which include the Constrained Steepest Decent (CSD) algorithm and the Constrained Conjugate Gradient algorithm (CCG) are deduced subject to a new constrain condition. They are both implemented in unitary transform domain. The computational complexities of the constrained algorithms are compared to those of the unconstrained algorithms. Resulting simulations show their performance comparisons.