Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Singular value decomposition and least squares solutions

This is a preview of subscription content, log in to check access.


  1. 1.

    Businger, P., Golub, G.: Linear least squares solutions by Householder transformations. Numer. Math.7, 269–276 (1965).

  2. 2.

    Forsythe, G. E., Henrici, P.: The cyclic Jacobi method for computing the principal values of a complex matrix. Proc. Amer. Math. Soc.94, 1–23 (1960).

  3. 3.

    — Golub, G.: On the stationary values of a second-degree polynomial on the unit sphere. J. Soc. Indust. Appl. Math.13, 1050–1068 (1965).

  4. 4.

    — Moler, C. B.: Computer solution of linear algebraic systems. Englewood Cliffs, New Jersey: Prentice-Hall 1967.

  5. 5.

    Francis, J.: TheQ R transformation. A unitary analogue to theL R transformation. Comput. J.4, 265–271 (1961, 1962).

  6. 6.

    Golub, G., Kahan, W.: Calculating the singular values and pseudo-inverse of a matrix. J. SIAM. Numer. Anal., Ser. B2, 205–224 (1965).

  7. 7.

    — Least squares, singular values, and matrix approximations. Aplikace Matematiky13, 44–51 (1968).

  8. 8.

    Hestenes, M. R.: Inversion of matrices by biorthogonalization and related results. J. Soc. Indust. Appl. Math.6, 51–90 (1958).

  9. 9.

    Kogbetliantz, E. G.: Solution of linear equations by diagonalization of coefficients matrix. Quart. Appl. Math.13, 123–132 (1955).

  10. 10.

    Kublanovskaja, V. N.: Some algorithms for the solution of the complete problem of eigenvalues. V. Vyčisl. Mat. i. Mat. Fiz.1, 555–570 (1961).

  11. 11.

    Martin, R. S., Reinsch, C., Wilkinson, J. H.: Householder's tridiagonalization of a symmetric matrix. Numer. Math.11, 181–195 (1968).

  12. 12.

    Wilkinson, J.: Error analysis of transformations based on the use of matrices of the formI-2w w H. Error in digital computation, vol. II, L.B. Rall, ed., p. 77–101. New York: John Wiley & Sons, Inc. 1965

  13. 13.

    — Global convergence ofQ R algorithm. Proceedings of IFIP Congress, 1968.

Download references

Author information

Additional information

Editor's note. In this fascicle, prepublication of algorithms from the Linear Algebra series of the Handbook for Automatic Computation is continued. Algorithms are published inAlgol 60 reference language as approved by the IFIP. Contributions in this series should be styled after the most recently published ones.

The work of this author was in part supported by the National Science Foundation and Office of Naval Research.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Golub, G.H., Reinsch, C. Singular value decomposition and least squares solutions. Numer. Math. 14, 403–420 (1970).

Download citation


  • Mathematical Method