Numerical analysis and scientific computation (Book, 2004) [University of Washington Libraries]
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Numerical analysis and scientific computation

Author: Jeffery J Leader
Publisher: Boston : Pearson Addison Wesley, ©2004.
Edition/Format:   Print book : EnglishView all editions and formats
This is a textbook in numerical analysis and scientific computing intended for students with a year of calculus coursework, and familiarity with matrix algebra and differential equations. Leader prefers not to introduce both mathematical topics and numerical techniques, so all the techniques in this book will be familiar to anyone with the prerequisites listed; for example, Leader chooses not to present the Fourier  Read more...
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Document Type: Book
All Authors / Contributors: Jeffery J Leader
ISBN: 0201734990 9780201734997 0321223357 9780321223357
OCLC Number: 53950725
Description: xiii, 590 pages : illustrations ; 24 cm
Contents: 1. Nonlinear Equations. Biscetion and Inverse Linear Interpolation.Newton's Method.The Fixed Point Theorem.Quadratic Convergence of Newton's Method.Variants of Newton's Method.Brent's Method.Effects of Finite Precision Arithmetic.Newton's Method for Systems.Broyden's Method.2. Linear Systems. Gaussian Elimination with Partial Pivoting.The LU Decomposition.The LU Decomposition with Pivoting.The Cholesky Decomposition.Condition Numbers.The QR Decomposition.Householder Triangularization and the QR Decomposition.Gram-Schmidt Orthogonalization and the QR Decomposition.The Singular Value Decomposition.3. Iterative Methods. Jacobi and Gauss-Seidel Iteration.Sparsity.Iterative Refinement.Preconditioning.Krylov Space Methods.Numerical Eigenproblems.4. Polynomial Interpolation. Lagrange Interpolating Polynomials.Piecewise Linear Interpolation.Cubic Splines.Computation of the Cubic Spline Coefficients.5. Numerical Integration. Closed Newton-Cotes Formulas.Open Newton-Cotes Formulas and Undetermined Coeffients.Gaussian Quadrature.Gauss-Chebyshev Quadrature.Radau and Lobatto Quadrature.Adaptivity and Automatic Integration.Romberg Integration.6. Differential Equations. Numerical Differentiation.Euler's Method.Improved Euler's Method.Analysis of Explicit One-Step Methods.Taylor and Runge-Kutta Methods.Adaptivity and Stiffness.Multi-Step Methods.7. Nonlinear Optimization. One-Dimensional Searches.The Method of Steepest Descent.Newton Methods for Nonlinear Optimization.Multiple Random Start Methods.Direct Search Methods.The Nelder-Mead Method.Conjugate Direction Methods.8. Approximation Methods. Linear and Nonlinear Least Squares.The Best Approximation Problem.Best Uniform Approximation.Applications of the Chebyshev Polynomials.Afterword. Bibliography. Answers. Index.
Responsibility: Jeffery J. Leader.


This text is intended for a first course in Numerical Analysis taken by students majoring in mathematics, engineering, computer science, and the sciences. This text emphasizes the mathematical ideas  Read more...
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