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Computing the generalized singular values/vectors of large sparse or structured matrix pairs

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We present a numerical algorithm for computing a few extreme generalized singular values and corresponding vectors of a sparse or structured matrix pair \(\{A,B\}\). The algorithm is based on the CS decomposition and the Lanczos bidiagonalization process. At each iteration step of the Lanczos process, the solution to a linear least squares problem with\((A^{\rm T},B^{\rm T})^{\rm T}\) as the coefficient matrix is approximately computed, and this consists the only interface of the algorithm with the matrix pair \(\{A,B\}\). Numerical results are also given to demonstrate the feasibility and efficiency of the algorithm.

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Received April 1, 1994 / Revised version received December 15, 1994

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Zha, H. Computing the generalized singular values/vectors of large sparse or structured matrix pairs . Numer. Math. 72, 391–417 (1996). https://doi.org/10.1007/s002110050175

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  • DOI: https://doi.org/10.1007/s002110050175

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