## Numerical Methods, Software, and AnalysisMathematics and computer science background. Numerical software. Errors, roud-off, and stabilitly. Models and formulas for numerical computations. Interpolation. Matrices and linear equations. Differentiation and integration. Nonlinear equations. Ordinary differential equations. Partial differential equations. Approximation of functions and data. Software practice, costs, and engineering. Software performance evaluation. The validation of numerical computations. Protran. |

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### Contents

MATH AND CS BACKGROUND | 1 |

DERIVATIVES INTEGRALS 15 PROTRAN | 7 |

NUMERICAL SOFTWARE | 15 |

Copyright | |

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accuracy ACM Algorithms algorithm analysis Apply approximation arithmetic B-spline band matrix basis functions boundary conditions break points calculation Chebyshev coefficients condition number Consider data set derivatives diagonal digits discretization discussed divided difference efficiency eigenvalues equation solver error estimates evaluate example factor Figure formula Fortran program Gauss elimination given gives Hermite cubic interpolation Hilbert matrix Hint IMSL library initial integration interpolation points interval knots least-squares library software linear equations linear functionals linear system LINPACK mathematical Muller's method multiple Newton Newton's method nonlinear equation norm numerical computation obtain orthogonal output parameters partial differential equation perturbations piecewise polynomials pivoting plot polynomial interpolation polynomials of degree pp(x regula falsi Repeat Problem representation right side root round-off error secant method Show simple smooth solving Ax spline interpolation statement step subprogram subroutine symmetric system of equations Taylor's series Theorem triangular values variables vector zero