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BIT Numerical Mathematics

, Volume 9, Issue 2, pp 167–173 | Cite as

Some comments on the solution of linear equations

  • R. P. Tewarson
  • B. Ramnath
Article

Abstract

Homogeneous, ill-conditioned and singular linear equations are considered and some methods for their solution are described.

Keywords

Linear Equation Computational Mathematic Singular Linear Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    A. Albert and R. W. Sittler,A method of Computing Least Square Estimators That Keep Up With The Data, SIAM J. On Control 3 (1965), pp. 1–31.CrossRefGoogle Scholar
  2. 2.
    Å. Björck,Solving Linear Least Squares Problems by Gram-Schmidt Orthogonalization, BIT, 7 (1967), pp. 1–21.Google Scholar
  3. 3.
    Å. Björck and G. H. Golub,Iterative Refinement of Linear Least Squares Solutions by Householder Transformations, BIT 7 (1967), pp. 322–337.Google Scholar
  4. 4.
    Å. Björck,Iterative Refinement of Linear Least Squares Solutions II, BIT 8 (1968), pp. 8–30.Google Scholar
  5. 5.
    V. N. Faddeeva,Shift for Systems With Badly Posed Matrices, Zh. Vych. Mat. Mat. Fiz. 5 (1965), pp. 907–911.Google Scholar
  6. 6.
    G. E. Forsythe and C. B. Moler,Computer Solution of Linear Algebraic Systems, Prentice-Hall, Inc., Englewood Cliffs, N.J. (1967), p. 10.Google Scholar
  7. 7.
    G. H. Golub,Numerical Methods for Solving Linear Least Squares Problems, Numer. Math., 7 (1965), pp. 206–216.CrossRefGoogle Scholar
  8. 8.
    J. B. Hawkins and A. Ben Israel,On Generalized Matrix Functions, System Research Memorandum, No. 193, The Technological Inst. Northwestern Univ. Jan. 1968.Google Scholar
  9. 9.
    A. Klinger,Approximate Pseudoinverse Solutions to Ill-Conditioned Linear Systems, J. Optimization Th. and Appl., 2 (1968), pp. 117–124.CrossRefGoogle Scholar
  10. 10.
    V. C. Kuznecov,Solution of a System of Linear Equations, Zh. Vych. Mat. Mat. Fiz. 7 (1967), pp. 157–160.Google Scholar
  11. 11.
    K. Levenberg,A Method for the Solution of Certain Non-Linear Problems in Least Squares, Quart. of Appl. Mat., 2 (1944), pp. 164–168.Google Scholar
  12. 12.
    E. E. Osborne,Smallest Least Square Solutions of Linear Equations, SIAM J. Num. Anal. 2 (1965), pp. 300–307.CrossRefGoogle Scholar
  13. 13.
    R. Penrose,On Best Approximate Solutions of Linear Matrix Equations, Proc. Cambridge Phil. Soc., 52 (1956), pp. 17–19.Google Scholar
  14. 14.
    J. Reblogle, B. H. Holcomb, and W. R. Burrus,The Use of Mathematical Programming for Solving Singular and Poorly Conditioned Systems of Equations, J. Math. Anal. Appl. 20 (1967), pp. 310–324.CrossRefGoogle Scholar
  15. 15.
    J. D. Riley,Solving Systems of Linear Equations with a Positive Definite, Symmetric, but Possibly Ill-Conditioned Matrix, MTAC, 9 (1956), pp. 96–101.Google Scholar
  16. 16.
    J. B. Rosen,Minimum and Basic Solutions to Singular Linear Systems, SIAM J., 12 (1964), pp. 156–162.Google Scholar
  17. 17.
    R. P. Tewarson,A Direct Method for Generalized Matrix Inversion, SIAM J. Num. Anal., 4 (1967), pp. 499–507.CrossRefGoogle Scholar
  18. 18.
    R. P. Tewarson,On The Orthonormalization of Sparse Vectors, Computing (1968), (to Appear).Google Scholar
  19. 19.
    J. H. Wilkinson,The Algebraic Eigenvalue Problem, London, Oxford University Press (1965), p. 152, 245.Google Scholar

Copyright information

© BIT Foundations 1969

Authors and Affiliations

  • R. P. Tewarson
    • 1
  • B. Ramnath
    • 1
  1. 1.State University of New YorkStony BrookUSA

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