Skip to main content

Using Interactive Graphical Computer Systems on Approximation Problems

  • Chapter
Iterationsverfahren Numerische Mathematik Approximationstheorie

Abstract

This paper gives a brief review of on-line graphical computer systems for mathematics and the advantages gained by such systems particulary in the area of approximation problems. This is followed by a description of PEG, an on-line graphical system for the solution of least squares approximation problems. Finally a discussion is given of other areas associated with approximation theory in which interactive graphics may be used to advantage.

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 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.99
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. Smith, L.B.: A survey of interactive graphical systems for mathematics. SLAC-PUB-540, Stanford Linear Accelerator Center, Standford, Califormia (Jan. 1969).

    Google Scholar 

  2. Culler, G.J. and B.D. Fried: An on-line computing center for scientific problems. Thompson Ramo Wooldrige Computer Division Report (now Bunker-Ramo Corp.) Canoga Park, California (1963).

    Google Scholar 

  3. Ruyle, A.: The development of systems for on-line mathematics at Harvard. Interactive Systems for Experimental Applied Mathematics (ed. by Klerer and Reinfelds), Acad.Press Inc., New York, N.Y. (1968), 241–254.

    Chapter  Google Scholar 

  4. Reinfelds, J., Flenker, L.A. and R.N. Seitz: AMTRAN, a remote-terminal, conversational-mode computer system. Proceedings 1966 ACM National Conference, Thompson Book Co., Washington, D.C. (1966), 469–477.

    Google Scholar 

  5. Stowe, A.N., Wiesen, R.A., Untema, D.B. and J.W. Forgie: The Lincoln Reckoner: An operation-oriented, on-line facility with distributed control. 1966 Spring Joint Computer Conference, Spartan Books, Washington, D.C, (1966), 433–444.

    Google Scholar 

  6. Kaplow, R., Strong, S., and J. Brackett: MAP, A System for on-line mathematical analysis. Report No. MAC-TR-24, Massachusetts Inst. of Technology (Jan. 1966).

    Google Scholar 

  7. Rice, J.R. and S. Rosen: NAPSS-a numerical analysis problem solving system. Proceedings-1966 ACM National Conference, Thompson Book Co., Washington, D.C, (1966), 51–56.

    Chapter  Google Scholar 

  8. Schlesinger, S. and L. Sashkin: POSE: A language for posing problems to a computer. Communications of the ACM, Vol.10, No.5 (May 1967), 279–285.

    Article  Google Scholar 

  9. Goodenough, J.B.: A lightpen-controlled program for on-line data analysis. Communications of the ACM, Vol.8, No. 2 (Febr. 1965), 130–134.

    Article  Google Scholar 

  10. Marchuk, G.I. and A.P. Yershov: Man-machine interaction in solving a certain class of differential equations. Proceedings of the IFIP Congress 65, Part II, (1965), 550-551.

    Google Scholar 

  11. Gear, C.W.: Numerical solution of ordinary differential equations at a remote terminal. Proceedings-1966 ACM National Conference, Thompson Book Co., Washington, D.C., 43-49.

    Google Scholar 

  12. Dixon, W.J.: Use of displays with packaged statistical programs. 1967 Fall Joint Computer Conference, Thompson Books, Washington, D.C., 481–484.

    Google Scholar 

  13. Smith, L.B.: The use of man-machine interaction in data-fitting problems. (Stanford Computer Science Ph.D. Thesis) SLAC Report No. 96, Stanford Linear Accelerator Center, Stanford, Califormia (March 1969).

    Google Scholar 

  14. Forsythe, G.E.: Generation and use of orthogonal polynomials for data-fitting with a digital computer. SIAM Journal, Vol, 5, No. 2 (June 1957), 74–88.

    Google Scholar 

  15. Ralston, A.: A First Course in Numerical Analysis. McGraw-Hill Book Co., New York (1965).

    Google Scholar 

  16. Hooke, R. and T.A. Jeeves: “Direct search” solution of numerical and statistical problems. Journ. of the ACM, Vol.8, No.2 (1961), 212–229.

    Article  Google Scholar 

  17. Remez, E.Y.: General Computational methods of Chebyshev Approximation. In The Problems with Linear Real Parameters, AEC-tr-4491, Books 1 and 2, English transl. by US AEC.

    Google Scholar 

  18. Golub, G.H. and L.B. Smith: Chebyshev Approximation of continuous functions by a Chebyshev system of functions. Techn.Rep. No. CS-72, Computer Science Department, Stanford Univ. (July 1967).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1970 Springer Basel AG

About this chapter

Cite this chapter

Smith, L.B. (1970). Using Interactive Graphical Computer Systems on Approximation Problems. In: Collatz, L., Meinardus, G., Unger, H., Werner, H. (eds) Iterationsverfahren Numerische Mathematik Approximationstheorie. Internationale Schriftenreihe zur Numerischen Mathematik / International Series of Numerical Mathematics / Série Internationale D’Analyse Numérique, vol 15. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5833-5_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-5833-5_20

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-5834-2

  • Online ISBN: 978-3-0348-5833-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics