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Computing the CS decomposition of a partitioned orthonormal matrix. (English) Zbl 0516.65016

MSC:
65F25 Orthogonalization in numerical linear algebra
15A23 Factorization of matrices
Software:
EISPACK; LINPACK
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References:
[1] Davis, C., Kahan, W.M.: The rotation of eigenvectors by a perturbation. III, SIAM J. Numer. Anal.7, 1-46 (1970) · Zbl 0198.47201 · doi:10.1137/0707001
[2] Daniel, J., Gragg, W.B., Kaufman, L., Stewart, G.W.: Reorthogonalization and stable algorithms for updating the Gram-SchmidtQR factorization. Math. Comput.30, 772-795 (1976) · Zbl 0345.65021
[3] Dongarra, J.J., Moler, C.B., Bunch, J.R., Stewart, G.W.: LINPACK User’s Guide. Society for Industrial and Applied Mathematics, Philadelphia, 1979
[4] Garbow, B.S., Boyle, J.M., Dongarra, J.J., Moler, C.B.: Matrix Eigensystem Routines ? EISPACK Guide Extensions. Lecture Notes Comput. Sci.51, 343 pages. Berlin, Heidelberg, New York: Springer 1977 · Zbl 0368.65020
[5] Paige, C.C., Saunders, M.A.: Toward a generalized singular value decomposition. SIAM J. Numer. Anal.18, 398-405 (1981) · Zbl 0471.65018 · doi:10.1137/0718026
[6] Rutishauser, H.: The Jacobi method for real symmetric matrices. Numer. Math.9, 1-10 (1966) · Zbl 0154.17002 · doi:10.1007/BF02165223
[7] Smith, B.T., Boyle, J.M., Dongarra, J.J., Garbow, B.S., Ikebe, Y., Klema, V.C., Moler, C.B.: Matrix Systems Routines ? EISPACK Guide. Lecture Notes Comput. Sci.6 (2d ed.), 551 pages. Berlin, Heidelberg, New York: Springer 1976 · Zbl 0325.65016
[8] Stewart, G.W.: Introduction to Matrix Computations. 441 pages. New York: Academic Press 1973 · Zbl 0302.65021
[9] Stewart, G.W.: On the perturbation of pseudo-inverses, projections and linear least squares problems. SIAM Rev.19, 634-662 (1977) · Zbl 0379.65021 · doi:10.1137/1019104
[10] Van Loan, C.F.: A general matrix eigenvalue algorithm. SIAM J. Numer. Anal.12, 819-834 (1975) · Zbl 0321.65023 · doi:10.1137/0712061
[11] Van Loan, C.F.: Generalizing the singular value decomposition. SIAM J. Numer. Anal.13, 76-83 (1976) · Zbl 0338.65022 · doi:10.1137/0713009
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