Skip to main content
SpringerLink
Log in

Minimax solution of n+1 inconsistent linear equations in n unknowns

Minimax-Lösung vonn+1 unverträglichen linearen Gleichungen inn Unbekannten

  • Published:
Computing Aims and scope Submit manuscript

Summary

An algorithm for computingChebyshev solution ofn+1 inconsistent linear equations inn unknowns is given. It makes use of orthogonal triangularization followed by the backsubstitution part of theGaussian elimination.

Zusammenfassung

Es wird ein Algorithmus zur Berechnung derTschebyscheff-Lösung vonn+1 linearen Gleichungen inn Unbekannten angegeben. Die Lösung wird gewonnen durch eine orthogonale Triangularization gefolgt durch den Teil der Rücksubstitution derGaussschen Elimination.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Cheney, E. W.: Introduction to Approximation Theory. p. 28–56. New York: McGraw-Hill Book Co. 1966.

    Google Scholar 

  2. Householder, A. S.: The Theory of Matrices in Numerical Analysis. p. 133–134. New York: Blaisdell Publishing Co. 1964.

    Google Scholar 

  3. Penrose, R.: A generalized inverse for matrices. Proc. Camb. Phil. Soc.,51, 406–413 (1955).

    Google Scholar 

  4. Penrose, R.: On best approximate solutions of linear matrix equations. Proc. Camb. Phil. Soc.,52, 17–19 (1956).

    Google Scholar 

  5. Tewarson, R. P.: On the orthonormalization of sparse vectors. Comp.3, 268–279 (1968).

    Article  Google Scholar 

  6. Tewarson, R. P.: On computing generalized inverses. Comp.4, 139–152 (1969).

    Article  Google Scholar 

  7. Wilkinson, J. H.: Error analysis of direct methods of matrix inversion. J. ACM.,8, 281–330 (1961).

    Article  Google Scholar 

  8. Wilkinson, J. H.: The Algebraic Eigenvalue Problem. pp. 152–153, 233–236. London: Oxford University Press. 1965.

    Google Scholar 

  9. Tewarson, R. P.: Minimax Solution ofn+1 Inconsistent Linear Equations inn Unknowns, Report No. 121, College of Engineering, State Univ. of N. Y. at Stony Brook, Sept. 16, 1968.

  10. Meicler, M.:Chebyshev Solution of an Inconsistent System ofn+1 Linear Equations inn Unknowns in Terms of its Least Squares Solutions. SIAM Rev.,10, 373–375 (1968).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Applied Analysis Department, State University of New York, 11790, Stony Brook, N. Y., USA

    Reginald P. Tewarson

Authors
  1. Reginald P. Tewarson
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was supported by the National Aeronautics and Space Administration, Washington, D. C., Grant No. NGR-33-015-013.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tewarson, R.P. Minimax solution of n+1 inconsistent linear equations in n unknowns. Computing 5, 371–376 (1970). https://doi.org/10.1007/BF02252331

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02252331

Keywords

Search

Navigation