Stoer J., Bulirsch R. Introduction To Numerical Analysis

3nd Edition. — Springer, 2002. — 746 p. — Series: Texts in Applied Mathematics (Book 12).
ISBN10: 038795452X.
ISBN13: 978-0387954523.
New edition of a well-known classic in the field; Previous edition sold over 6000 copies worldwide; Fully-worked examples; Many carefully selected problems.
The book contains a large amount of information not found in standard textbooks. Written for the advanced undergraduate/beginning graduate student, it combines the modern mathematical standards of numerical analysis with an understanding of the needs of the computer scientist working on practical applications. Among its many particular features are:
fully worked-out examples;
many carefully selected and formulated problems;
fast Fourier transform methods;
a thorough discussion of some important minimization methods;
solution of stiff or implicit ordinary differential equations and of differential algebraic systems;
modern shooting techniques for solving two-point boundary-value problems;
basics of multigrid methods.
Included are numerous references to contemporary research literature.