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Addison-Wesley / Prentice Hall

Mathematics

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Numerical Analysis and Scientific Computation
Jeffery J. LeaderRose-Hulman Institute of Technology

ISBN-10: 0201734990
ISBN-13:  9780201734997

Publisher:  Addison-Wesley
Copyright:  2005
Format:  Cloth; 608 pp
Published:  02/05/2004
Status: Instock


Suggested retail price: $128.00
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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 behind the methods and the idea of mixing methods for robustness. The optional use of MATLAB is incorporated throughout the text.

  • Quick introduction to numerical methods, with round-off error and computer arithmetic deferred until students have had experience with real algorithms.
  • Modern approach to numerical linear algebra.
  • Explanation of numerical techniques from MATLAB and other programs and subroutine libraries.
  • Appropriate mix of numerical analysis theory and practical scientific computation principles.
  • Greater than usual emphasis on optimization.
  • Extensive numerical experiments so students can gain experience.
  • Efficient and unobtrusive introduction to MATLAB.



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.

Instructor's Solutions Manual
Brown & Haynes
©2005 | Addison-Wesley | Electronic Supplement; 320 pp | Instock
ISBN-10: 0321257324 | ISBN-13: 9780321257321
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ISBN-10: 0321257332 | ISBN-13: 9780321257338
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