Least Squares Problems

  • Heinz Rutishauser


We consider once again a system of nonlinear equations
$$\begin{array}{*{20}{c}} {{f_1}\left( {{x_1},{x_2}, \cdots ,{x_p}} \right) = 0} \\ {{f_2}\left( {{x_1},{x_2}, \cdots ,{x_p}} \right) = 0} \\ \vdots \\ {{f_n}\left( {{x_1},{x_2}, \cdots ,{x_p}} \right) = 0,} \end{array}$$
but now assume that the number n of equations is larger than the number pof unknowns.


Nash Lawson 


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  1. Björck, A. [1967]: Solving linear least squares problems by Gram-Schmidt orthogonalization, BIT 7, 1–21.MATHCrossRefGoogle Scholar
  2. Dennis, J.E. and Schnabel, R.B. [1983]: Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Englewood Cliffs, N.J.MATHGoogle Scholar
  3. Dongarra, J.J., Moler, C.B., Bunch, J.R. and Stewart, G.W. [1979]: LINPACK Users’ Guide, SIAM, Philadelphia.Google Scholar
  4. Fletcher, R. [1987]: Practical Methods of Optimization, 2nd ed., Wiley, Chichester.MATHGoogle Scholar
  5. Gill, P.E., Murray, W. and Wright, M.H. [1981]: Practical Optimization, Academic Press, London.MATHGoogle Scholar
  6. Golub, G.H. and Van Loan, C.F. [1989]: Matrix Computations, 2nd ed., The Johns Hopkins University Press, Baltimore.MATHGoogle Scholar
  7. Higham, N.J. and Stewart, G.W. [1987]: Numerical linear algebra in statistical computing, in State of the Art in Numerical Analysis (A. Iserles and M.J.D. Powell, eds.), pp. 41–57. Clarendon Press, Oxford.Google Scholar
  8. IMSL [1987]: Math/Library User’s Manual, Houston.Google Scholar
  9. Kahaner, D., Moler, C. and Nash, S. [1989]: Numerical Methods and Software, Prentice- Hall, Englewood Cliffs, N.J.MATHGoogle Scholar
  10. Lawson, C.L. and Hanson, R.J. [1974]: Solving Least Squares Problems, Prentice-Hall, Englewood Cliffs, N.J.MATHGoogle Scholar
  11. Moré, J.J. [1977]: The Levenberg-Marquardt algorithm: implementation and theory, in Numerical Analysis (G.A. Watson, ed.), Lecture Notes Math. 630, pp. 105–116, Springer, New York.Google Scholar
  12. Moré, J.J., Garbow, B.S. and Hillstrom, K.E. [1980]: User Guide for MINPACK-1, Argonne National Laboratory, Report ANL-80–74.Google Scholar
  13. Rice, J.R. [1966]: Experiments on Gram-Schmidt orthogonalization, Math. Comp. 20, 325–328.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Birkhäuser Boston 1990

Authors and Affiliations

  • Heinz Rutishauser

There are no affiliations available

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