id: 05152725
dt: b
an: 2010c.00514
au: Kügler, Phillipp; Windsteiger, Wolfgang
ti: Algorithmic methods. Numbers, vectors, polynomials. (Algorithmische
Methoden. Zahlen, Vektoren, Polynome.)
so: Mathematik Kompakt. Basel: Birkhäuser (ISBN 978-3-7643-8434-0/pbk). xii,
160~p. (2009).
py: 2009
pu: Basel: Birkhäuser
la: DE
cc: N35 N45 U25
ut: algorithms; numerical linear algebra; numerical analysis; computer algebra
ci:
li:
ab: Algorithmic methods are useful tools for solving technical, scientific, or
industrial problems. Typically, the problem at hand is specified as a
mathematical problem and a suitable algorithm for solving it is
desired. The algorithm is then often expressed and executed as a
computer program with appropriate data representations and
program-using techniques. The algorithmic method for solving problems
requires expertise in several areas such as numerical methods or
computer algorithms and efficient programming. This book for students
in their first or second year presents the basic knowledge necessary
for applying the methods to different problems. The first chapter
nicely presents many basic concepts for problem solving with
algorithms, such as specification, iterative algorithms, rounding
errors, discretization, recursion, norms, stability, or complexity. The
next three chapters cover concepts and algorithms for numbers, vectors,
or univariate polynomials, respectively. A second volume will cover
functions, matrices, and multivariate polynomials, respectively. The
presentation of these chapters also includes relevant concepts from
analysis, linear algebra, numerical analysis, algorithm design,
programming, and other aspects of computer science. For algorithms, a
pseudocode as well as the implementation for a computer is discussed,
often separated into computer representations of the aspects and
programming techniques. The presentation is given in mathematical
rigorous style and no further reading seems to be required to read the
text or design a course. The book is written in German. The underlying
course was designed for students of technical mathematics, but is as
well suited for computer science students in the area of scientific
computing.
rv: Thomas Rauber (Bayreuth)