عنوان

Numerical Analysis in Modern Scientific Computing

(Number (ISBN

9780387215846

(Number (ISBN

9781441929907

Number

b402312

Title Proper

Numerical Analysis in Modern Scientific Computing

General Material Designation

[Book]

Other Title Information

An Introduction /

First Statement of Responsibility

by Peter Deuflhard, Andreas Hohmann.

Edition Statement

Second Edition.

Place of Publication, Distribution, etc.

New York, NY :

Name of Publisher, Distributor, etc.

Springer New York,

Date of Publication, Distribution, etc.

2003.

Series Title

Texts in Applied Mathematics,

Volume Designation

43

ISSN of Series

0939-2475 ;

Text of Note

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 -- Exercises -- 6 Three-Term Recurrence Relations -- 6.1 Theoretical Background -- 6.2 Numerical Aspects -- 6.3 Adjoint Summation -- Exercises -- 7 Interpolation and Approximation -- 7.1 Classical Polynomial Interpolation -- 7.2 Trigonometric Interpolation -- 7.3 Bézier Techniques -- 7.4 Splines -- Exercises -- 8 Large Symmetric Systems of Equations and Eigenvalue Problems -- 8.1 Classical Iteration Methods -- 8.2 Chebyshev Acceleration -- 8.3 Method of Conjugate Gradients -- 8.4 Preconditioning -- 8.5 Lanczos Methods -- Exercises -- 9 Definite Integrals -- 9.1 Quadrature Formulas -- 9.2 Newton-Cotes Formulas -- 9.3 Gauss-Christoffel Quadrature -- 9.4 Classical Romberg Quadrature -- 9.5 Adaptive Romberg Quadrature -- 9.6 Hard Integration Problems -- 9.7 Adaptive Multigrid Quadrature -- Exercises -- References -- Software.

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Text of Note

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.

International Standard Book Number

9781441929907

Title

Springer eBooks

Computer science-- Mathematics.

Engineering.

Mathematics.

Numerical analysis.

Deuflhard, P., (Peter)

Hohmann, Andreas.

SpringerLink (Online service)

Date of Transaction

20190307160400.0

Electronic name

[Book]

Y