The improvement of the successive projections method having the optimum solution in the Chebyshev sense

In the previous successive projections (SP) method, we obtained the solution satisfying the prescribed allowable deviation from the desired frequency response. However, this solution is not necessarily an optimum in the Chebyshev sense. In this paper, we propose the improvement of the SP method so that the obtained solution becomes an optimum in the Chebyshev sense. Then, in the proposed method, the average of local maximum error in the nth iteration is selected as the maximum allowable deviation in the next iteration. The algorithm is iterated until the absolute maximum error between the desired frequency response and designed response becomes equiripple.