## Numerical AnalysisThis well-respected text gives an introduction to the modern approximation techniques and explains how, why, and when the techniques can be expected to work. The authors focus on building students' intuition to help them understand why the techniques presented work in general, and why, in some situations, they fail. With a wealth of examples and exercises, the text demonstrates the relevance of numerical analysis to a variety of disciplines and provides ample practice for students. The applications chosen demonstrate concisely how numerical methods can be, and often must be, applied in real-life situations. In this edition, the presentation has been fine-tuned to make the book even more useful to the instructor and more interesting to the reader. Overall, students gain a theoretical understanding of, and a firm basis for future study of, numerical analysis and scientific computing. A more applied text with a different menu of topics is the authors' highly regarded NUMERICAL METHODS, Third Edition. |

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Solve the following equation using Newton-Raphson method:

𝑥2−4𝑥2+4=0

### Contents

Mathematical Preliminaries and Error Analysis | 1 |

Solutions of Equations in One Variable | 47 |

Interpolation and Polynomial Approximation | 105 |

Numerical Differentiation and Integration | 173 |

InitialValue Problems for Ordinary Differential Equations | 259 |

Direct Methods for Solving Linear Systems | 357 |

Iterative Techniques in Matrix Algebra | 431 |

Approximation Theory | 497 |

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2012 Cengage Learning actual solution Algorithm approximate the solution boundary-value problem compute convergence copied Copyright 2012 Cengage cubic spline derivative determine diagonal differential equation Due to electronic duplicated eBook and/or eChapter(s eigenvalues eigenvectors electronic rights endpoints entries eopied error bound Euler’s method evaluations Example Exercise Set ﬁrst formula Gauss-Seidel method Gaussian elimination given gives implies initial approximation initial-value problems integral interpolating polynomial interval least squares linear system Maple matrix Newton’s method nodes nonlinear nonzero norm number of iterations obtained orthogonal OUTPUT party eontent rnay polynomial of degree procedure quadrature Repeat Exercise requires Rights Reserved rnay be suppressed round-off error Runge-Kutta method scanned seanned_ Secant method Section sequence Show sinx solve Step Suppose Table Taylor polynomial technique Theorem third party content truncation error vector whole wi+1 y(ti zero