Parameterized eigensolution technique for solving constrained least squares problemsFootnote^∗

^∗This work is supported by Kuwait university contract number SM 158.

References

• Abdel-Aziz , M. R. 1999 . Solving constrained least squares problems parametrically, Far East . J. of Mathematical Science , 1 ( 1 ) : 79 – 94 .
   Google Scholar
• Bj[otilde]rck , Å. Least squares methods , Philadelphia : SIAM .
   Google Scholar
• Golub , G. H. and Van Loan , C. F. 1996 . Matrix Computations , 3rd edn. , The Johns Hopkins University Press .
   Google Scholar
• Abdel-Aziz , M. R. 1994 . Safeguarded Use of Implicit Restarted Lanczos Technique for Solving Nonlinear Structural Eigensystems . International Journal of Numerical Methods in Engineering , 37 : 3117 – 3133 .
   Google Scholar
• Bj[otilde]rck , Å. , Grimme , E. and Van Dooren , P. 1994 . An implicit shift bidiagonalization algorithm for ill-posed systems . BIT , 34 : 510 – 534 .
   Google Scholar
• Sorensen D. C. Minimizaion of a large scale quadratic function subject to an ellipsoidal constraint TR94-27, Houston, Texas 77251-1829. Dept. of Comp. & Appl. Math., Rice Univ 1994
   Google Scholar
• Hansen , P. C. 1992 . Analysis of discrete ill-posed problems by means of the L-curve . SIAM Review , 34 : 561 – 580 .
   Web of Science ®Google Scholar
• James , D. 1992 . Implicit nullspace iterative method for constrained least squares problems . SIAM J. Matrix Anal Appl. , 13 ( 3 ) : 962 – 978 .
   Web of Science ®Google Scholar
• Golub , G. H. and Von Matt , U. 1991 . Quadratically constrained least squares and quadratic problems . Num. Math. , 59 : 561 – 580 .
   Web of Science ®Google Scholar
• Plato , R. and Vainikko , G. 1990 . On the regularization of projection methods for solving ill-posed problems . Numer. Math. , 57 : 63 – 79 .
   Web of Science ®Google Scholar
• Sorensen , D. C. 1990 . Implicit application of polynomial filters in a k-step Arnoldi method . SIAM J. on Matrix Analysis and Applications , 13 ( 1 ) : 357 – 385 .
   Web of Science ®Google Scholar
• Van Loan , C. F. 1985 . On the method of weighting for equality-constrained least-squares problems . SIAM J. of Numer. Anal , 22 ( 5 ) : 851 – 864 .
   Web of Science ®Google Scholar
• Moré , J. J. and Sorensen , D. C. 1983 . Computing a trust region step . SIAM J. on Scientific and Stat. Computing , 4 : 553 – 572 .
   Web of Science ®Google Scholar
• Sorensen , D. C. 1982 . Newton's method with a model trust region modification . SIAM. J. Numer. Anal , 19 ( 2 ) : 409 – 426 .
   Web of Science ®Google Scholar
• Gander , W. 1981 . Least squares with quadratic constraint . Num. Math. , 36 : 291 – 307 .
   Web of Science ®Google Scholar
• Parlett , B. N. 1980 . Symmetric eigenvalue problem , Englewood Cliffs, NJ : Prentice-Hall .
   Google Scholar
• Lawson , C. L. and Hanson , R. J. Solving least squares problems , Englewood Cliffs, NJ : Prentice-Hall .
   Google Scholar