Introduction to numerical analysis. Translated from the German by R. Bartels, W. Gautschi and C. Witzgall. 2. ed. (English) Zbl 0771.65002

Stoer, J.; Bulirsch, R.

Texts in Applied Mathematics. 12. New York: Springer-Verlag. xiii, 660 p. (1993).

[For the first edition (1980) see Zbl 0423.65002).]
The new edition of this well written book is enlarged by the following topics: \(B\)-splines and their computation, elimination methods for large sparse systems of linear equations, Lanczos algorithm for eigenvalue problems, implicit shift techniques for the \(LR\) and \(QR\) algorithm, implicit differential equations, differential algebraic systems, new methods for stiff differential equations, preconditioning techniques and convergence rate of the conjugate gradient algorithm and multigrid methods for boundary value problems.
Cf. also the reviews of the German original editions [Einführung in die Numerische Mathematik I, II; (1972; Zbl 0245.65001 and 1973; Zbl 0257.65001)].

Reviewer: L.Berg (Rostock)

MSC:

65-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis
65G50	Roundoff error
65Dxx	Numerical approximation and computational geometry (primarily algorithms)
65Fxx	Numerical linear algebra
65Hxx	Nonlinear algebraic or transcendental equations
65Lxx	Numerical methods for ordinary differential equations

Keywords:

error analysis; interpolation; integration; linear equations; zeros; eigenvalues; ordinary differential equations; iterations; textbook