## Numerical Analysis, Volume 1Provides a foundation in modern approximation techniques and explains how, why and when they can be expected to work. This edition places greater emphasis on providing applied problems from diverse areas so that students understand how numerical methods are used in real-life situations. |

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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