Rutishauser Heinz. Lectures on Numerical Mathematics

Birkhauser, 1990. — 558 p. — ISBN13: 978-1-4612-8035-4.The present book is an edition of the manuscripts to the courses "Numerical Methods I" and "Numerical Mathematics I and II" which Professor H. Rutishauser held at the E.T.H. in Zurich. The first-named course was newly conceived in the spring semester of 1970, and intended for beginners, while the two others were given repeatedly as elective courses in the sixties. For an understanding of most chapters the fundamentals of linear algebra and calculus suffice. In some places a little complex variable theory is used in addition. However, the reader can get by without any knowledge of functional analysis.
The first seven chapters discuss the direct solution of systems of linear equations, the solution of nonlinear systems, least squares problems, interpolation by polynomials, numerical quadrature, and approximation by Chebyshev series and by Remez' algorithm. The remaining chapters include the treatment of ordinary and partial differential equations, the iterative solution of linear equations, and a discussion of eigenvalue problems. In addition, there is an appendix dealing with the qdalgorithm and with an axiomatic treatment of computer arithmetic. For a few algorithms, also problems of programming are discussed and fragments of ALGOL-programs are given. It should be pointed out that a number of complete and safe procedures to the methods described here are to be published (also with Birkhiiuser, as Vol. 33 of the International Series of Numerical Mathematics) by W. Gander, L. Molinari and H. §vecova under the title "Numerische Prozeduren aus Nachlass und Lehre von Prof. Heinz Rutishauser".