CDMA is becoming an increasingly popular multiplexing scheme in wireless communications and this has necessitated the development of efficient detection techniques. The exponential complexity of the optimal detector on one end and inferior performance of conventional single-user detctor at the other have led to the development of suboptimal multiuser detectors with lower complexity. Most of these detection techniques involve solution of a linear system. In their naive implementation this requires O(n³) operations in the size of the matrix. This cost can be reduced if we move towards modern iterative techniques for solution of the system. However maximum benefit can be achieved if we fully exploit the structure of the system. In this paper we have proposed several methods of reducing the computational complexity utilizing the above ideas. We have also come up with algorighms which computationally can achieve the lower bound in complexity.