## Numerical computation |

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### Contents

in a computer 5 1 4 Errors in arithmetic operations 6 1 5 Errors of compu | 14 |

2 9 Systems of nonlinear equations 34 Bibliographic notes | 35 |

3 4 Complete solution of a polynomial 43 3 5 Methods | 51 |

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### Common terms and phrases

accuracy algorithm analysis arithmetic binary calculation Chapter Chebyshev polynomials chosen coefficients column consider corresponding defined derivative difference table differential equations digits discussed divided difference eigenvalues eigenvector error term evaluated finite finite-difference formula function values Gauss-Seidel method gaussian elimination given in Example gives the value initial approximation instability integration interpolation interval involved Isaacson and Keller iterative methods large number least-squares mathematical matrix McCracken and Dorn multiplication multistep methods Newton's method nomial nonzero normally obtained operations orthogonal polynomials orthogonality property over-relaxation pivotal points xt poly polynomial of degree possible problem quadratic factor Ralston range rate of convergence reader relative error right-hand side roots round-off error Runge-Kutta methods scheme set of equations shown Simpson's rule solved stability step stiff equations Sturm sequence subtraction suitable Taylor series tridiagonal true solution various vector zero