## Numerical analysis, Volume 1This 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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### Contents

Mathematical Preliminaries | 1 |

Solutions of Equations in One Variable | 47 |

Interpolation and Polynomial Approximation | 104 |

Copyright | |

12 other sections not shown

### Common terms and phrases

actual solution Algorithm applied approximate the solution Bisection method boundary conditions boundary-value problem calculations coefficients Composite Simpson's rule compute considered constant convergence cubic spline defined derivative determine diagonal differential equation eigenvalues eigenvector endpoints entries error bound Euler's method evaluations EXAMPLE EXERCISE SET factorization Figure Finite-Difference formula function Gauss-Seidel method Gaussian elimination given gives implies initial approximation initial-value problem integral interpolating polynomial interval Lagrange polynomial least squares linear system Maple matrix maximum number Newton's method nodes nonsingular norm number of iterations obtained OUTPUT partial-differential equation points polynomial of degree positive definite Procedure completed successfully quadratic quadrature real numbers Repeat Exercise requires roundoff error Runge-Kutta method Secant method Section sequence Show Simpson's rule solve Step 1 Set subroutine Suppose symmetric Taylor polynomial technique Theorem Trapezoidal rule tridiagonal truncation error unique solution vector zero