Abstract
Numerical analysis is a broad subject area that permeates modern technology and education in the sciences, engineering, economics, and operations research. We examine the historical roots of the subject, outline the three constituent areas, and give a personal perspective on some important work.
References
Ackleh AS, Allen EJ, Kearfott RB, Seshaiyer P (2010) Classical and modern numerical analysis. CRC Numerical Analysis and Scientific Computing, Chapman & Hall. CRC Press, 2000 N.W. Corporate Blvd., Boca Raton, FL 33431-9868, USA, theory, methods and practice
Anderson E, Bai Z, Bischof C, Demmel J, Dongarra J, Croz JD, Greenbaum A, Hammarling S, McKenney A, Ostrouchov S, Sorensen D (1992) LAPACK’s user’s guide. Society for Industrial and Applied Mathematics. updated editions are available, Philadelphia, PA
de Boor C (1978) A practical guide to splines. Springer, New York
Burat E (1885) Traité D’Arithmétique a L’usage des élèves des lycées et colléges. Eugéne Belin et Fils., Paris, found November 16, 2020 at https://gallica.bnf.fr/ark:/12148/bpt6k202612w.texteImage
Butcher J (1996) A history of runge-kutta methods. Appl Numer Math 20(3):247–260. https://doi.org/10.1016/0168-9274(95)00108-5. URL http://www.sciencedirect.com/science/article/pii/0168927495001085
Casselman B (2012) Archimedes on the circumference and area of a circle. Web page, URL http://www.ams.org/publicoutreach/feature-column/fc-2012-02. Accessed 18 Jan 2021. (The copyright on Archimedes’ original treatise has probably expired, though)
Cheney EW (1966) Introduction to approximation theory. McGraw–Hill, New York
Dennis JE Jr, Schnabel RB (1996) Numerical methods for unconstrained optimization and nonlinear equations. In: Classics in applied mathematics, vol 16. SIAM, Philadelphia, PA, originally published by Prentice–Hall, 1983
Dongarra JJ, Moler CB, Bunch JR, Stewart GW (1979) LINPACK users’ guide. SIAM, Philadelphia
Euler L (1768) Institutionum Calculi Integralis. Impensis Academiae Imperialis Scientiarum Petropoli, retrieved in PDF from https://ia802205.us.archive.org/28/items/institutionescal020326mbp/institutionescal020326mbp.pdf on 20 Jan 2021)
Fibonacci L (1202) Liber abaci (book of calculation). Handwritten Manuscript, excerpts found at https://www.maa.org/book/export/html/841546 on 20 Jan 2021
Forsythe GE, Malcolm MA, Moler CB (1977) Computer methods for mathematical computations. Prentice–Hall Professional Technical Reference
Gauss C (1809) Theoria motus corporum coelestium in sectionibus conicis solem ambientium. Carl Friedrich Gauss Werke, Hamburgi sumptibus Frid. Perthes et I.H.Besser, URL https://books.google.com/books?id=ORUOAAAAQAAJ, eBook and PDF currently available free of charge from Google at https://books.google.com/books/about/Theoria_motus_corporum_coelestium_in_sec.html?id\unhbox\voidb@x\hbox{$=$}ORUOAAAAQAAJ
Golub GH, van Loan CF (1996) Matrix computations, 3rd edn. Johns Hopkins University Press
IEEE-754 (2019) IEEE 754–2019, standard for floating-point arithmetic. IEEE, New York. https://doi.org/10.1109/IEEESTD.2019.876622
Isaacson E, Keller HB (1994) Analysis of numerical methods. Dover, New York. ebook available; originally published by John Wiley & Sons, 1966
Kutta W (1901) Beitrag zur näherungsweisen Integration totaler Differentialgleichungen. Zeit Math Phys 46:435–453
Leibniz G (1703) Explication de l’arithmtique binaire. Mem lAcad R Sci 3:85–93
Leibniz GW (1684) Nova methodus pro maximis et minimis, itemque tangentibus, quae nec fractas, nec irrationales quantitates moratur, et singulare pro illis calculi genus. Acta Eruditorum:467–473
Nash SG (ed) (1990) A history of scientific computing. Association for Computing Machinery, New York, NY, USA
Newton I (1687) Philosophiae naturalis principia mathematica. J Societatis Regiae ac Typis J. Streater, URL https://books.google.com/books?id=-dVKAQAAIAAJ, in Latin. Retrieved in PDF f on 19 Jan 2021
Ortega JM (1972) Numerical analysis: a second course. Academic Press, New York
Richardson LF (1922) Weather prediction by numerical process. Cambridge University Press. URL https://archive.org/details/weatherpredictio00richrich
Runge C (1895) Ueber die numerische Auflösung von Differentialgleichungen. Math Ann 46:167–178
Schnellinger J (1879) Das gekürzte Rechnen (basically, truncated arithmetic or inexact arithmetic). Zeitschrift für das Realschulwesen 1879:257–284, (currently available in Google Books)
Schumaker L (2007) Spline functions: basic theory, 3rd. Cambridge Mathematical Library, Cambridge University Press, DOI https://doi.org/10.1017/CBO9780511618994, first edition published by WileyInterscience, 1980 Sigler LELE (2002) Fibonacci’s Liber Abaci: A Translation into Modern English of Leonardo Pisano’s Book of Calculation. Sources and studies in the history of mathematics and physical sciences. Springer-Verlag, Berlin/Heidelberg/London, etc
Strang G, Fix GJ (1973) An analysis of the finite element method. Prentice-Hall, Englewood Cliffs
Taylor B (1715) Methodus incrementorum directa et inversa. Londini, retrieved in PDF from https://ia800900.us.archive.org/6/items/UFIE003454_TO0324_PNI-2529_000000/UFIE003454_TO0324_PNI-2529_000000.pdf on 20 Jan 2021
Wilkinson J (1965) The algebraic eigenvalue problem. Clarendon Press, Oxford
Wilkinson JH (1963) Rounding errors in algebraic processes. Prentice–Hall, Englewood Cliffs
Young DM (1971) Iterative solution of large linear systems. Academic Press
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Science+Business Media LLC
About this entry
Cite this entry
Kearfott, R.B. (2021). Some Remarks on the Foundations of Numerical Analysis. In: Meyers, R.A. (eds) Encyclopedia of Complexity and Systems Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27737-5_749-1
Download citation
DOI: https://doi.org/10.1007/978-3-642-27737-5_749-1
Received:
Accepted:
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-27737-5
Online ISBN: 978-3-642-27737-5
eBook Packages: Springer Reference Physics and AstronomyReference Module Physical and Materials ScienceReference Module Chemistry, Materials and Physics