## A First Course in Numerical AnalysisThis outstanding text by two well-known authors treats numerical analysis with mathematical rigor, but presents a minimum of theorems and proofs. Oriented toward computer solutions of problems, it stresses error analysis and computational efficiency, and compares different solutions to the same problem. Following an introductory chapter on sources of error and computer arithmetic, the text covers such topics as approximation and algorithms; interpolation; numerical differentiation and numerical quadrature; the numerical solution of ordinary differential equations; functional approximation by least squares and by minimum-maximum error techniques; the solution of nonlinear equations and of simultaneous linear equations; and the calculation of eigenvalues and eigenvectors of matrices. This second edition also includes discussions of spline interpolation, adaptive integration, the fast Fourier transform, the simplex method of linear programming, and simple and double QR algorithms. Problems — some strictly mathematical, others requiring a computer — appear at the end of each chapter. |

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### Contents

INTRODUCTION AND PRELIMINARIES | 1 |

APPROXIMATION AND ALGORITHMS | 31 |

INTERPOLATION | 52 |

NUMERICAL DIFFERENTIATION NUMERICAL QUADRATURE AND SUMMATION | 89 |

THE NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS | 164 |

FUNCTIONAL APPROXIMATION LEASTSQUARES TECHNIQUES | 247 |

FUNCTIONAL APPROXIMATION MINIMUM MAXIMUM ERROR TECHNIQUES | 285 |

THE SOLUTION OF NONLINEAR EQUATIONS | 332 |

THE SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS | 410 |

THE CALCULATION OF EIGENVALUES AND EIGENVECTORS OF MATRICES | 483 |

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abscissas accuracy algebra applied arithmetic assume bound calculate Chap chapter Chebyshev polynomials coefficients column consider convergence corrector corresponding deduce defined derive determine diagonal difference digital computer discussed eigenvalues eigenvectors elements equal error term estimate evaluate example floating-point follows Gaussian elimination given Hessenberg Householder's method initial approximation interpolation formula interval inverse iterative methods Lagrangian interpolation linear equations magnitude Math mathematical matrix maximum error multiplications Newton-Cotes Newton-Cotes formulas Newton's Newton's method norm numerical analysis orthogonal orthogonal polynomials polynomial of degree positive problem QR algorithm quadrature formula rational function Ref.i right-hand side roots roundoff error Runge-Kutta methods satisfies secant method sequence Show solve spline stability step subintervals symmetric symmetric matrix tabular points technique theorem tion transformation trapezoidal rule triangular tridiagonal true value truncation error variable vector why?l zero