Abstract
The most important principles of numerical analysis will be the subject of this chapter. The solution of practical problems usually requires the application of a professional numerical library of numerical methods, developed for computers. Some of them will be introduced at the end of Section 19.8.3. Special computer algebra systems such as Mathematica and Maple will be discussed with their numerical programs in Chapter 20, p. 953 and in Section 19.8.4, p. 946. Error propagation and computation errors will be examined in Section 19.8.2, p. 939.
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19. Numerical Analysis
Brenner, S.C.; Scott, L.R.: The Mathematical Theory of Finite Element Methods. — Springer-Verlag 1994.
Chapra, S.C.; Canale, R.P.: Numerical Methods for Engineers. — McGraw Hill 1989.
Collatz, L.: Numerical Treatment of Differential Equations. — Springer-Verlag 1966.
Davis, P.J.; Rabinowitz, P: Methods of Numerical Integration. — Academic Press 1984.
De Boor, C.: A Practical Guide to Splines. — Springer-Verlag 1978.
Golub, G.; Ortega, J.M.: Scientific Computing. — B. G. Teubner 1996.
Grossmann, Ch.; Roos, H.-G.: Numerik partieller Differentialgleichungen. — B. G. Teubner 1992.
Hackbusch, W.: Elliptic Differential Equations. — Springer-Verlag 1992.
Hämmerlin, G.; Hoffmann, K.-H.: Numerische Mathematik. — Springer-Verlag 1994.
Hairer, E.; Norsett, S.P.; Wanner, G.: Solving Ordinary Differential Equations. Vol. 1: Nonstiff Problems. Vol. 2: Stiff and Differential Problems. Vol. 3: Algebraic Problems. — Springer-Verlag 1994.
Heitzinger, W.; Troch, I.; Valentin, G.: Praxis nichtlinearer Gleichungen. — C. Hanser Verlag 1984.
Kiełbasiński, A.; Schwetlick, H.: Numerische lineare Algebra. Eine computerorientierte Einführung. — Verlag H. Deutsch 1988.
Knothe, K.; Wessels, H.: Finite Elemente. Eine Einführung für Ingenieure. — Springer-Verlag 1992.
Kress, R.: Numerical Analysis. — Springer-Verlag 1998.
Lancaster, P.; Salkauska, S.K.: Curve and Surface Fitting. — Academic Press 1986.
Maess, G.: Vorlesungen über numerische Mathematik, Bd. 1, 2. — Akademie-Verlag 1984–1988.
Meinardus, G.: Approximation von Funktionen und ihre numerische Behandlung. — Springer-Verlag 1964.
NÜrnberger, G.: Approximation by Spline Functions. — Springer-Verlag 1989.
Pao, Y.-C: Engineering Analysis. — Springer-Verlag 1998.
Quarteroni, A.; Valli, A.: Numerical Approximation of Partial Differential Equations. — Springer-Verlag 1994.
Reinsch, Chr.: Smoothing by Spline Functions. — Numer. Math. 1967.
Schwarz, H.R.: Methode der finiten Elemente. — B. G. Teubner 1984.
Schwarz, H.R.: Numerische Mathematik. — B. G. Teubner 1986.
Schwetlick, H.; Kretzschmar, H.: Numerische Verfahren für Naturwissenschaftler und Ingenieure. — Fachbuchverlag 1991.
Stoer, J.; Bulirsch, R.: Introduction to Numerical Analysis. — Springer-Verlag 1993.
Stroud, A.H.: Approximate Calculation of Multiple Integrals. — Prentice Hall 1971.
TÖRNIG, W.: Numerische Mathematik für Ingenieure und Physiker, Bd. 1, 2. — Springer-Verlag 1990.
Überhuber, C: Numerical Computation 1, 2. — Springer-Verlag 1997.
Willers, F.A.: Methoden der praktischen Analysis. — Akademie-Verlag 1951.
Zurmühl, R.: Praktische Mathematik für Ingenieure und Physiker. — Springer-Verlag 1984.
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(2007). Numerical Analysis. In: Handbook of Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72122-2_19
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