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Computation of the Cholesky decomposition of the autocorrelation matrix is essential in developing zero-forcing, minimum mean square error (MMSE), and decision feedback detectors for a long code-division multiple-access (CDMA) system. However, computing the Cholesky decomposition of the time-varying correlation matrix requires many computer operations. This is because the computation of the filter weights is segment specific (varies from one symbol interval to next). In this paper, a novel and fast algorithm is developed to compute the Cholesky decomposition of the autocorrelation matrix for a long-code CDMA system. The smart update algorithms, to compute the solution (filter weights) of one segment from the solution of the previous segment, reduce the computational complexity, particularly for large-sized autocorrelation matrices. We exploit the fact that the channel matrix of a long-code CDMA system is block banded with a shift structure. Although the channel matrix is not Toeplitz for a long-code CDMA system, the shift structure of the matrix, along with its banded structure, allows the development of fast smart update recursive algorithms for data estimation. The relevance of this algorithm is discussed for channels with multipath delays extending over many symbol intervals. Simulations show that the proposed algorithm performs the same as competing multiuser detector algorithms for long-code CDMA at much reduced computational complexity.