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Computing theCS decomposition of a partitioned orthonormal matrix

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Summary

This paper describes an algorithm for simultaneously diagonalizing by orthogonal transformations the blocks of a partitioned matrix having orthonormal columns.

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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)

    Google Scholar 

  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)

    Google Scholar 

  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

    Google Scholar 

  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

    Google Scholar 

  5. Paige, C.C., Saunders, M.A.: Toward a generalized singular value decomposition. SIAM J. Numer. Anal.18, 398–405 (1981)

    Article  Google Scholar 

  6. Rutishauser, H.: The Jacobi method for real symmetric matrices. Numer. Math.9, 1–10 (1966)

    Google Scholar 

  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

    Google Scholar 

  8. Stewart, G.W.: Introduction to Matrix Computations. 441 pages. New York: Academic Press 1973

    Google Scholar 

  9. Stewart, G.W.: On the perturbation of pseudo-inverses, projections and linear least squares problems. SIAM Rev.19, 634–662 (1977)

    Article  Google Scholar 

  10. Van Loan, C.F.: A general matrix eigenvalue algorithm. SIAM J. Numer. Anal.12, 819–834 (1975)

    Article  Google Scholar 

  11. Van Loan, C.F.: Generalizing the singular value decomposition. SIAM J. Numer. Anal.13, 76–83 (1976)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, University of Maryland, 20742, College Park, MD, USA

    G. W. Stewart

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  1. G. W. Stewart
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Additional information

This work was supported by the Air Force Office of Scientific Research under Contract No. AFOSR-82-0078

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Stewart, G.W. Computing theCS decomposition of a partitioned orthonormal matrix. Numer. Math. 40, 297–306 (1982). https://doi.org/10.1007/BF01396447

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  • DOI: https://doi.org/10.1007/BF01396447

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