## Numerical Analysis in Modern Scientific Computing: An IntroductionMathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the clas sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathe matical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs. |

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### Contents

Linear Systems | 1 |

Error Analysis | 21 |

Linear LeastSquares Problems | 57 |

Nonlinear Systems and LeastSquares Problems | 81 |

Exercises | 113 |

Linear Eigenvalue Problems | 119 |

ThreeTerm Recurrence Relations | 151 |

Interpolation and Approximation | 179 |

Large Symmetric Systems of Equations and Eigenvalue | 237 |

Definite Integrals | 269 |

Exercises | 321 |

Software | 331 |

### Other editions - View all

Numerical Analysis in Modern Scientific Computing: An Introduction Andreas Hohmann,Peter Deuflhard No preview available - 2010 |

Numerical Analysis in Modern Scientific Computing: An Introduction Andreas Hohmann,Peter Deuflhard No preview available - 2012 |

### Common terms and phrases

According to Theorem algorithm approximation error B-splines backward analysis basis Bernstein polynomials Bezier points cg-method Chebyshev nodes Chebyshev polynomials Cholesky column pivoting componentwise computation convergence corresponding cubic denote derivative determined diagonal matrix differential equations eigenvalue problem eigenvector estimate Euclidean evaluation Example Exercise factorization Figure function Gauss-Newton method Gaussian elimination given Hermite interpolation input integral integrand interpolation polynomial interval invertible Lagrange polynomials Lemma linear least-squares problem linear system mapping Matm,n(R Matn(R minimal solution multiplications Newton Newton's method nodes nonlinear norm obtain orthogonal matrix orthogonal polynomials parameter perturbation precision Proof quadrature formula relative condition number respect Romberg quadrature satisfies scalar product Section sequence singular values solve Spd-matrix spline stability indicator starting values statement step size H symmetric symmetric matrix three-term recurrence relation transformation trapezoidal sum triangular matrix trigonometric uniquely upper triangular vector well-conditioned xk+i