Details

Autor(en) / Beteiligte

• Stoer, J
• Bulirsch, R

Titel

Introduction to Numerical Analysis [electronic resource]

Auflage

1st ed. 1980

Ort / Verlag

New York, NY : Springer New York

Erscheinungsjahr

1980

Link zum Volltext

• SpringerLink Books - AutoHoldings

Beschreibungen/Notizen

• Bibliographic Level Mode of Issuance: Monograph
• Includes bibliographical references and index.
• 1 Error Analysis -- 2 Interpolation -- 3 Topics in Integration -- 4 Systems of Linear Equations -- 5 Finding Zeros and Minimum Points by Iterative Methods -- 6 Eigenvalue Problems -- 7 Ordinary Differential Equations -- 8 Iterative Methods for the Solution of Large Systems of Linear Equations. Some Further Methods -- General Literature on Numerical Methods.
• This book is based on a one-year introductory course on numerical analysis given by the authors at several universities in Germany and the United States. The authors concentrate on methods which can be worked out on a digital computer. For important topics, algorithmic descriptions (given more or less formally in ALGOL 60), as well as thorough but concise treatments of their theoretical foundations, are provided. Where several methods for solving a problem are presented, comparisons of their applicability and limitations are offered. Each comparison is based on operation counts, theoretical properties such as convergence rates, and, more importantly, the intrinsic numerical properties that account for the reliability or unreliability of an algorithm. Within this context, the introductory chapter on error analysis plays a special role because it precisely describes basic concepts, such as the numerical stability of algorithms, that are indispensable in the thorough treatment of numerical questions. The remaining seven chapters are devoted to describing numerical methods in various contexts. In addition to covering standard topics, these chapters encompass some special subjects not usually found in introductions to numerical analysis. Chapter 2, which discusses interpolation, gives an account of modem fast Fourier transform methods. In Chapter 3, extrapolation techniques for spe~ding up the convergence of discretization methods in connection with Romberg integration are explained at length.
• English