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A concise introduction to numerical analysis

Author: A C Faul
Publisher: Boca Raton : CRC Press, Taylor & Francis Group, [2016] ©2016
Edition/Format:   Print book : EnglishView all editions and formats

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Genre/Form: Textbooks
Document Type: Book
All Authors / Contributors: A C Faul
ISBN: 9781498712187 1498712185
OCLC Number: 923794111
Notes: "A Chapman & Hall book."
Description: xv, 292 pages : illustrations ; 24 cm
Contents: Fundamentals Floating Point Arithmetic Overflow and Underflow Absolute, Relative Error, Machine Epsilon Forward and Backward Error Analysis Loss of Significance Robustness Error Testing and Order of Convergence Computational Complexity Condition Revision Exercises Linear Systems Simultaneous Linear Equations Gaussian Elimination and Pivoting LU Factorization Cholesky Factorization QR Factorization The Gram-Schmidt Algorithm Givens Rotations Householder Reflections Linear Least Squares Singular Value Decomposition Iterative Schemes and Splitting Jacobi and Gauss-Seidel Iterations Relaxation Steepest Descent Method Conjugate Gradients Krylov Subspaces and Pre-Conditioning Eigenvalues and Eigenvectors The Power Method Inverse Iteration Deflation Revision Exercises Interpolation and Approximation Theory Lagrange Form of Polynomial Interpolation Newton Form of Polynomial Interpolation Polynomial Best Approximations Orthogonal polynomials Least-Squares Polynomial Fitting The Peano Kernel Theorem Splines B-Spline Revision Exercises Non-Linear Systems Bisection, Regula Falsi, and Secant Method Newton's Method Broyden's Method Householder Methods Muller's Method Inverse Quadratic Interpolation Fixed Point Iteration Theory Mixed Methods Revision Exercises Numerical Integration Mid-Point and Trapezium Rule The Peano Kernel Theorem Simpson's Rule Newton-Cotes Rules Gaussian Quadrature Composite Rules Multi-Dimensional Integration Monte Carlo Methods Revision Exercises ODEs One-Step Methods Multistep Methods, Order, and Consistency Order Conditions Stiffness and A-Stability Adams Methods Backward Differentiation Formulae The Milne and Zadunaisky Device Rational Methods Runge-Kutta Methods Revision Exercises Numerical Differentiation Finite Differences Differentiation of Incomplete or Inexact Data PDEs Classification of PDEs Parabolic PDEs Elliptic PDEs Parabolic PDEs in Two Dimensions Hyperbolic PDEs Spectral Methods Finite Element Method Revision Exercises
Responsibility: A.C. Faul, University of Cambridge, UK.
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"This is a thorough and detailed introduction to the important topic of numerical analysis. It is based upon an existing successful postgraduate course and assumes a significant level of mathematical Read more...

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