Numerical Analysis in Modern Scientific Computing
Springer-Verlag New York Inc.
978-0-387-95410-3 (ISBN)
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.
Erscheint lt. Verlag | 14.1.2003 |
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Reihe/Serie | Texts in Applied Mathematics ; 43 |
Zusatzinfo | XVIII, 340 p. |
Verlagsort | New York, NY |
Sprache | englisch |
Maße | 156 x 234 mm |
Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
Mathematik / Informatik ► Mathematik ► Analysis | |
Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
ISBN-10 | 0-387-95410-4 / 0387954104 |
ISBN-13 | 978-0-387-95410-3 / 9780387954103 |
Zustand | Neuware |
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