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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Smith, L.B.: A survey of interactive graphical systems for mathematics. SLAC-PUB-540, Stanford Linear Accelerator Center, Standford, Califormia (Jan. 1969).
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).
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.
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.
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.
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).
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.
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.
Goodenough, J.B.: A lightpen-controlled program for on-line data analysis. Communications of the ACM, Vol.8, No. 2 (Febr. 1965), 130–134.
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.
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.
Dixon, W.J.: Use of displays with packaged statistical programs. 1967 Fall Joint Computer Conference, Thompson Books, Washington, D.C., 481–484.
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).
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.
Ralston, A.: A First Course in Numerical Analysis. McGraw-Hill Book Co., New York (1965).
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.
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.
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).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights 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