Numerical Analysis in Modern Scientific Computing : An Introduction

This introductory book directs the reader to a selection of useful elementary numerical algorithms on a reasonably sound theoretical basis, built up within the text. The primary aim is to develop algorithmic thinking-emphasizing long-living computational concepts over fast changing software issues....

Full description

Main Authors: Deuflhard, Peter, Hohmann, Andreas (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY Springer New York 2003, 2003
Edition:2nd ed. 2003
Series:Texts in Applied Mathematics
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
LEADER 03695nmm a2200421 u 4500
001 EB000614677
003 EBX01000000000000000467759
005 00000000000000.0
007 cr|||||||||||||||||||||
008 140122 ||| eng
020 |a 9780387215846 
100 1 |a Deuflhard, Peter 
245 0 0 |a Numerical Analysis in Modern Scientific Computing  |h Elektronische Ressource  |b An Introduction  |c by Peter Deuflhard, Andreas Hohmann 
250 |a 2nd ed. 2003 
260 |a New York, NY  |b Springer New York  |c 2003, 2003 
300 |a XVIII, 340 p  |b online resource 
505 0 |a 1 Linear Systems -- 1.1 Solution of Triangular Systems -- 1.2 Gaussian Elimination -- 1.3 Pivoting Strategies and Iterative Refinement -- 1.4 Cholesky Decomposition for Symmetric Positive Definite Matrices -- Exercises -- 2 Error Analysis -- 2.1 Sources of Errors -- 2.2 Condition of Problems -- 2.3 Stability of Algorithms -- 2.4 Application to Linear Systems -- Exercises -- 3 Linear Least-Squares Problems -- 3.1 Least-Squares Method of Gauss -- 3.2 Orthogonalization Methods -- 3.3 Generalized Inverses -- Exercises -- 4 Nonlinear Systems and Least-Squares Problems -- 4.1 Fixed-Point Iterations -- 4.2 Newton Methods for Nonlinear Systems -- 4.3 Gauss-Newton Method for Nonlinear Least-Squares Problems -- 4.4 Nonlinear Systems Depending on Parameters -- Exercises -- 5 Linear Eigenvalue Problems -- 5.1 Condition of General Eigenvalue Problems -- 5.2 Power Method -- 5.3 QR-Algorithm for Symmetric Eigenvalue Problems -- 5.4 Singular Value Decomposition -- 5.5 Stochastic Eigenvalue Problems 
653 |a Computational Mathematics and Numerical Analysis 
653 |a Probability Theory and Stochastic Processes 
653 |a Computational intelligence 
653 |a Computational Intelligence 
653 |a Algebra 
653 |a Computer mathematics 
653 |a Algebra 
653 |a Mathematical physics 
653 |a Numerical analysis 
653 |a Numerical Analysis 
653 |a Theoretical, Mathematical and Computational Physics 
653 |a Probabilities 
700 1 |a Hohmann, Andreas  |e [author] 
710 2 |a SpringerLink (Online service) 
041 0 7 |a eng  |2 ISO 639-2 
989 |b SBA  |a Springer Book Archives -2004 
490 0 |a Texts in Applied Mathematics 
856 |u https://doi.org/10.1007/978-0-387-21584-6?nosfx=y  |x Verlag  |3 Volltext 
082 0 |a 518 
520 |a This introductory book directs the reader to a selection of useful elementary numerical algorithms on a reasonably sound theoretical basis, built up within the text. The primary aim is to develop algorithmic thinking-emphasizing long-living computational concepts over fast changing software issues. The guiding principle is to explain modern numerical analysis concepts applicable in complex scientific computing at much simpler model problems. For example, the two adaptive techniques in numerical quadrature elaborated here carry the germs for either exploration methods or multigrid methods in differential equations, which are not treated here. The presentation draws on geometrical intuition wherever appropriate, supported by large number of illustrations. Numerous exercises are included for further practice and improved understanding. This text will appeal to undergraduate and graduate students as well as researchers in mathematics, computer science, science, and engineering. At the same time, it is addressed to practical computational scientists who, via self-study, wish to become acquainted with modern concepts of numerical analysis and scientific computing on an elementary level. The sole prerequisite is undergraduate knowledge in linear algebra and calculus