Theory and Applications of Numerical Analysis

2nd Edition

Print ISBN: 9780125535601
eBook ISBN: 9780080519128
Imprint: Academic Press
Published Date: 5th July 1996
Page Count: 447
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This text is a self-contained Second Edition, providing an introductory account of the main topics in numerical analysis. The book emphasizes both the theorems which show the underlying rigorous mathematics andthe algorithms which define precisely how to program the numerical methods. Both theoretical and practical examples are included.

Key Features

@bul:* a unique blend of theory and applications

  • two brand new chapters on eigenvalues and splines
  • inclusion of formal algorithms
  • numerous fully worked examples
  • a large number of problems, many with solutions


Advanced undergraduate students in math, computer science, engineering and physical sciences

Table of Contents

(Chapter Heading): Introduction. Basic Analysis. Taylors Polynomial and Series. The Interpolating Polynomial. Best Approximation. Splines and Other Approximations. Numerical Integration and Differentiation. Solution of Algebraic Equations of One Variable. Linear Equations. Matrix Norms and Applications. Matrix Eigenvalues and Eigenvectors. Systems of Non-linear Equations. Ordinary Differential Equations. Boundary Value and Other Methods for Ordinary Differential Equations. Appendices. Solutions to Selected Problems. References. Subject Index.

Introduction: What is Numerical Analysis? Numerical Algorithms. Properly Posed and Well-Conditioned Problems. Basic Analysis: Functions. Limits and Derivatives. Sequences and Series. Integration. Logarithmic and Exponential Functions. Taylor's Polynomial and Series: Function Approximation. Taylor's Theorem. Convergence of Taylor Series. Taylor Series in Two Variables. Power Series. The Interpolating Polyomial: Linear Interpolation. Polynomial Interpolation. Accuracy of Interpolation. The Neville–Aitken Algorithm. Inverse Interpolation. Divided Differences. Equally Spaced Points. Derivatives and Differences. Effect of Rounding Error. Choice of Interpolation Points. Examples of Bernstein and Runge. "Best"Approximation: Norms of Functions. Best Approximations. Least Squares Approximations. Orthogonal Functions. Orthogonal Polynomials. Minimax Approximation. Chebyshev Series. Economization of Power Series. The Remez Algorithms. Further Results on Minimax Approximation.Splines and Other Approximations: Introduction. B-Splines. Equally-Spaced Knots. Hermite Interpolation. Pade and Rational Approximation. Numerical Integration and Differentiation: Numerical Integration. Romberg Integration. Gaussian Integration. Indefinite Integrals. Improper Integrals. Multiple Integrals. Numerical Differe


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© Academic Press 1996
Academic Press
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@qu:The first edition was an outstanding work, and the additions that have been put in the Second Edition are very appropriate and have been written up in exemplary fashion. @source:--Philip J. Davis