Linear multiuser detectors have been developed for CDMA systems to maintain a balance between the performance and computational complexity of the detectors. However for a system with a large number of users and huge data block length, the cubic complexity of these naive algorithms is computationally prohibitive for real time estimation of transmitted data bits. In this thesis we have proposed methods to reduce the amount of computation by following two approaches. We have divided the problem into smaller subproblems and then solved these subproblems individually. We have found that pipelining and windowing techniques applied to linear feedback detectors can reduce the total amount of computation, without significantly sacrificing the performance. Secondly, we have proposed two novel algorithms which exploit the block-Toeplitz structure of the correlation matrix and solve the linear system in only O(NK\sp2) steps. Finally, in a practical system, the delays associated with the users and hence the correlation matrix vary dynamically. We have shown methods to update the solution of the system based on the previous results and the rank of the perturbations of the system. We have also computed a threshold for the number of users whose delays can vary, beyond which fresh computation of the solution of the system is less expensive than the updating scheme.