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Many multiple-input multiple-output (MIMO) applications require the computation of some or all of the nonzero singular values and the corresponding left and right singular vectors of a time-varying channel response matrix. An adaptive algorithm is derived to achieve this goal, based on a first-order perturbation, which updates a full or partial singular value decomposition (SVD) using input and noisy output vectors. The updates can be computed recursively, resulting in a highly efficient algorithm that has lower complexity than the earlier least-mean-square (LMS)-based algorithm and achieves better performance at low signal-to-noise ratio (SNR). The performance is demonstrated using measured MIMO channel data obtained in an urban microcellular environment.