Skip to main content

Some determinantal identities in a vector space, with applications

  • Conference paper
  • First Online:
Padé Approximation and its Applications Bad Honnef 1983

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1071))

Abstract

The determinantal identities of Al. Magnus, J.J. Sylvester and F.F. Schweins are extended to determinants whose first row consists of elements of a vector space and whose other rows are formed by scalars. These identities are then used to derive a recursive algorithm having many applications.

Work performed under the NATO Research Grant O27.81

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. C. BREZINSKI A general extrapolation algorithm Numer. Math., 35 (1980) 175–187.

    Article  MathSciNet  MATH  Google Scholar 

  2. C. BREZINSKI The Mühlbach-Neville-Aitken algorithm and some extensions. BIT, 20 (1980) 444–451.

    Article  MathSciNet  MATH  Google Scholar 

  3. C. BREZINSKI Recursive interpolation, extrapolation and projection. J. Comp. Appl. Math., submitted.

    Google Scholar 

  4. V.N. FADDEEVA Computational methods of linear algebra. Dover, New-York, 1959.

    MATH  Google Scholar 

  5. T. HÅVIE Generalized Neville type extrapolation schemes. BIT, 19 (1979) 204–213.

    Article  MathSciNet  MATH  Google Scholar 

  6. P. HENRICI Elements of numerical analysis. Wiley, New-York, 1964.

    MATH  Google Scholar 

  7. Al. MAGNUS Fractions continues généralisées: théorie et applications. Thèse, Université Catholique de Louvain, 1976.

    Google Scholar 

  8. G. MEINARDUS, G.D. TAYLOR Lower estimates for the error of best uniform approximation. J. Approx. Theory, 16 (1976) 150–161.

    Article  MathSciNet  MATH  Google Scholar 

  9. G. MÜHLBACH The general Neville-Aitken algorithm and some applications. Numer. Math., 31 (1978) 97–110.

    Article  MathSciNet  MATH  Google Scholar 

  10. J.B. ROSEN The gradient projection method for nonlinear programming. Part I. Linear constraints. J. SIAM, 8 (1960) 181–217.

    MATH  Google Scholar 

  11. C. SCHNEIDER Vereinfachte Rekursionen zur Richardson-Extrapolation in Spezialfällen. Numer. Math., 24 (1975) 177–184.

    Article  MathSciNet  MATH  Google Scholar 

  12. J. WIMP Sequence transformations and their applications. Academic Press, New-York, 1981.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Helmut Werner Hans Josef Bünger

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer-Verlag

About this paper

Cite this paper

Brezinski, C. (1984). Some determinantal identities in a vector space, with applications. In: Werner, H., Bünger, H.J. (eds) Padé Approximation and its Applications Bad Honnef 1983. Lecture Notes in Mathematics, vol 1071. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099606

Download citation

  • DOI: https://doi.org/10.1007/BFb0099606

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13364-3

  • Online ISBN: 978-3-540-38914-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics