## Numerical Analysis: A Mathematical IntroductionThis book provides professionals and students with a thorough understanding of the interface between mathematics and scientific computation. Ranging from classical questions to modern techniques, it explains why numerical computations succeed or fail. The book is divided into four sections, with an emphasis on the use of mathematics as a tool in determining the success rate of numerical methods. The text requires only a modest level of mathematical training, and is ideally suited for scientists and students in mathematics, physics and engineering. |

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### Contents

The entrance fee | 1 |

A flavour of numerical analysis | 11 |

Algebraic preliminaries | 25 |

Polynomial and trigonometric approximation | 47 |

Leastsquares approximation for polynomials | 77 |

Splines | 106 |

Fouriers world | 133 |

Quadrature | 165 |

Pythagoras world | 290 |

Nonlinear problems | 305 |

Nonlinear equations and systems | 331 |

Solving differential systems | 362 |

Singlestep schemes | 385 |

Linear multistep schemes | 414 |

Towards partial differential equations | 439 |

479 | |

### Other editions - View all

Numerical Analysis: A Mathematical Introduction M. Schatzman,Michelle Schatzman No preview available - 2002 |

### Common terms and phrases

algebra algorithm approximation Assume B-splines basis block bounded calculate column Consequently construct continuous function convergence deduce defined denote diagonal differential equations dimension divided differences eigenvalues eigenvectors equal error estimate Euler scheme Exercise finite floating-point Fourier series give given Hermitian Hermitian matrix Hessenberg identity inequality initial condition integral interpolation polynomial interval invertible invertible matrix iterative method knots Lemma linear system LU decomposition modulus multiplication multistep Newton's method nonzero norm notation numerical analysis obtain operator norm orthogonal orthogonal polynomials orthonormal polynomial of degree positive definite problem Proof properties prove quadrature formula real number relation respect result satisfies scalar product sequence Show solution of eqn solve spectral radius splines stable strictly positive Subsection Suppose tends to infinity Theorem triangular matrix trigonometric polynomials unique upper triangular vanishes variable vector space zero