Numerische Mathematik / Eine algorithmisch orientierte Einführung

This textbook on numerics/scientific computing has developed into a classic in the German-speaking countries. It deals with the basics of the numerics of linear and non-linear equation systems, interpolation and approximation, integration as well as eigenvalue problems. The fourth edition was supplemented by a section on higher-dimensional Monte Carlo methods. The only basic knowledge assumed is of analysis and linear algebra.

Zusammenfassung
All known languages of the world have special lexical units called names or proper names, whose purpose is to designate the individuality of single persons, groups of people, families, places, hills, mountains, rivers, and animals, as well as things and institutions, etc. The study of names, also called onomastics or onomatology, is not simply a subdiscipline of linguistics; several other disciplines besides traditional philology cooperate in the study. The universe of names as objects of research lacks any clear-cut limits. The interest in names can be linguistic or philosophical, historical or contemporary, theoretical or practical, legal or political, ethnographic or religious; and in each of these and other cases, interest can concentrate on a single language, a group of languages, or a family of them. The present volume is the work of more than 250 authors from 42 countries. This fact alone shows how widespread the studies are. The three languages used in the volume (English, French, German) give only a partial impression of the supranational and transcultural character of the names and their studies. Among the main areas on which the volume concentrates are the following: Specifities of names as linguistic signs, and their systematic analysis; Idiosyncrasies of name studies in various countries in the past and present; The multiplicity of names and their properties in as many languages as was practical; Demonstration of the basic functional identity, yet endless formal variety, of names as identifiers of individual entities; The phenomena of change and assimilation that occur in contact between two or more languages; The importance of names in disciplines other than linguistics, such as history, law, philosophy, theology, geography, archeology, and many others; Names and their use in connection and interaction with other areas of human activities in society; Numerous case studies showing the variety of approaches and methods that must be applied if microanalyses of sets of data are to be used for important conclusions; Registers of names belonging to more than 50 languages of the world, which should make accessible this whole plethora of material and ideas, through their articulation (topical, onomatological, etc.) and the arrangement of material; 23 chapters which are systematically ordered according to specific characteristics of names and their study.

Inhalt
Frontmatter -- Vorwort -- Inhaltsverzeichnis -- Überblick -- 1 Lineare Gleichungssysteme -- 2 Fehleranalyse -- 3 Lineare Ausgleichsprobleme -- 4 Nichtlineare Gleichungssysteme und Ausgleichsprobleme -- 5 Lineare Eigenwertprobleme -- 6 Drei-Term-Rekursionen -- 7 Interpolation und Approximation -- 8 Große symmetrische Gleichungssysteme und Eigenwertprobleme -- 9 Bestimmte Integrale -- Software -- Literatur -- Index