## Numerical Methods, Software, and AnalysisNumerical Methods, Software, and Analysis, Second Edition introduces science and engineering students to the methods, tools, and ideas of numerical computation. Introductory courses in numerical methods face a fundamental problem—there is too little time to learn too much. This text solves that problem by using high-quality mathematical software. In fact, the objective of the text is to present scientific problem solving using standard mathematical software. This book discusses numerous programs and software packages focusing on the IMSL library (including the PROTRAN system) and ACM Algorithms.The book is organized into three parts. Part I presents the background material. Part II presents the principal methods and ideas of numerical computation. Part III contains material about software engineering and performance evaluation. A uniform approach is used in each area of numerical computation. First, an intuitive development is made of the problems and the basic methods for their solution. Then, relevant mathematical software is reviewed and its use outlined. Many areas provide extensive examples and case studies. Finally, a deeper analysis of the methods is presented as in traditional numerical analysis texts. |

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### Contents

NUMERICAL SOFTWARE | 19 |

ERRORS ROUNDOFF AND STABILITY | 39 |

MODELS AND FORMULAS FOR NUMERICAL COMPUTATION | 69 |

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accuracy ACM Algorithms Algorithm analysis Apply approximation arithmetic array B-spline band matrix basis functions boundary conditions break points calculation CALL Chebyshev coefficients columns condition number CUBIC SPLINE data set defined derivatives digits discretization discussed divided difference DOUBLE PRECISION eigenvalues equation solver error estimate Euler's method evaluate example factor Figure finite difference formula Fortran program Gauss elimination given gives Hint IMSL library IMSL program IMSL ROUTINE input integration interpolation points interval iteration knots least-squares Library Application library program linear equations linear system LINPACK mathematical Newton Newton's method nonlinear equation norm obtain orthogonal output parameters partial differential equation piecewise polynomials plot polynomial interpolation PROTRAN random number REAL representation RETURN END right side roots round-off error secant method Show simple smooth solution solving Ax squares statement step subprogram SUBROUTINE symmetric system of equations Table Taylor's series Theorem trapezoidal rule variables vector WRITE(6 zero