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rank-revealing method and its application

An Efficient and Accurate Parallel Algorithm for the Singular Value Problem of Bidiagonal Matrices

this paper we propose an algorithm based on Laguerre's iteration, rank two divide-and-conquer technique and a hybrid strategy for computing singular values of bidiagonal matrices. The algorithm is fully parallel in nature and evaluates singular values to tiny relative error if necessary. It is competitive with QR algorithm in serial mode in speed and advantageous in computing partial singular values. Error analysis and numerical results are presented

method. SIAM Review, 21:339-360, 1979.

[2] P. A. Businger. Numerically stable deflation of Hessenberg and symmetric tridiagonal matrices. BIT, 11:262-270, 1971. [3] J. Cuppen. A divide and conquer method for the symmetric tridiagonal eigenproblem. Numer. Math., 36:177-195, 1981