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Least squares with a quadratic constraint

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Summary

We present the theory of the linear least squares problem with a quadratic constraint. New theorems characterizing properties of the solutions are given. A numerical application is discussed.

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References

  1. Elden, L.: Algorithms for the regularisation and constrained least squares methods. Bit17, 134–145 (1977)

    Google Scholar 

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

    Google Scholar 

  3. Gander, W.: On the linear least squares problem with a quadratic constraint. Habilitationsschrift ETH Zürich. STAN-CS-78-697, Stanford University, 1978

  4. Golub, G.H., Heath, M., Wahba, G.: Generalized cross-validation. Technometrics21, 215–223 (1979)

    Google Scholar 

  5. Kahan, W.: Manuscript in Box 5G of the G. Forsythe Archive, Stanford Main Library (∼1965)

  6. Lawson, C.L., Hanson, R.J.: Solving least squares problems. Englewood Cliffs, N.J.: Prentice Hall 1974

    Google Scholar 

  7. Marquardt, D.W.: An algorithm for least-squares estimation of nonlinear parameters. SIAM J. Appl. Math.11, 431–441 (1963)

    Google Scholar 

  8. Moré, J.J.: The Levenberg-Marquardt algorithm: implementation and theory. Dundee Conference on Numerical Analysis (1977)

  9. Reinsch, C.H.: Smoothing by spline functions. Numer. Math.10, 177–183 (1967)

    Google Scholar 

  10. Rutishauser, H.: Once again: the least square problem. Linear Algebra and Appl.1, 479–488 (1968)

    Google Scholar 

  11. Rutishauser, H.: Vorlesungen über Numerische Mathematik. (M. Gutknecht, Hrsg.) Basel: Birkhäuser 1976

    Google Scholar 

  12. Spjøtvoll, E.: A note on a théorem of Forsythe and Golub. SIAM J. Appl. Math.23, 307–311 (1972)

    Google Scholar 

  13. Tikhonov, A.N., Arsenin, V.Y.: Solution of ill posed problems. New York: Wiley, 1977

    Google Scholar 

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

    Google Scholar 

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Authors and Affiliations

  1. Neu-Technikum, CH-9470, Buchs, Switzerland

    Walter Gander

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  1. Walter Gander
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Gander, W. Least squares with a quadratic constraint. Numer. Math. 36, 291–307 (1980). https://doi.org/10.1007/BF01396656

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  • DOI: https://doi.org/10.1007/BF01396656

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