## Numerical Methods: For Computer Science, Engineering, and Mathematics |

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### Contents

Mathematical Preliminaries | 1 |

The Solution of Nonlinear Equations fx 0 | 42 |

Direct Methods for Solving Linear Systems | 105 |

Copyright | |

10 other sections not shown

### Common terms and phrases

abscissas accuracy Algorithm approximation augmented matrix binary bisection method Boole's rule calculations Chebyshev polynomials compute Cond converges cubic data points diagonal differential equation digits eigenvalue eigenvector ENDIF endpoints error bound error term Euler's method evaluate Example Exercises factor Figure fixed point fixed-point iteration formula function f(x function values Gauss-Legendre rule given graph Hence Heun's method INPUT interval involving Lagrange interpolation Lagrange polynomial least-squares linear system method to find midpoint minimum multiple Newton polynomial Newton-Raphson Newton's method nodes x0 obtain partial derivatives Pn(x polynomial of degree PRINT quadratic quotient real number result Romberg integration root round-off error Runge-Kutta method secant method Section sequence Show Simpson's rule solution curve solve spline starting value step size h subintervals Suppose Table Taylor polynomial Theorem tion trapezoidal rule truncation error upper-triangular system variables Verify Write a report Xk yk zero