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Numerical Analysis in Modern Scientific Computing

An Introduction
BuchGebunden
340 Seiten
Englisch
Springererschienen am14.01.20032nd ed.
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the clas­ sical techniques of applied mathematics.mehr
Verfügbare Formate
BuchGebunden
EUR106,99
BuchKartoniert, Paperback
EUR79,13
E-BookPDF1 - PDF WatermarkE-Book
EUR76,99

Produkt

KlappentextMathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the clas­ sical techniques of applied mathematics.
Details
ISBN/GTIN978-0-387-95410-3
ProduktartBuch
EinbandartGebunden
Verlag
Erscheinungsjahr2003
Erscheinungsdatum14.01.2003
Auflage2nd ed.
ReiheTexts in Applied Mathematics
Seiten340 Seiten
SpracheEnglisch
Gewicht733 g
IllustrationenXVIII, 340 p.
Artikel-Nr.10540802

Inhalt/Kritik

Inhaltsverzeichnis
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.mehr

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