## Theoretical Numerical Analysis: A Functional Analysis FrameworkMathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scienti?c disciplines and a resurgence of interest in the modern as well as the cl- 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). Thedevelopmentofnewcoursesisanaturalconsequenceofahighlevelof 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 Ma- ematical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs. |

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### Contents

1 | |

Linear Operators on Normed Spaces 51 | 50 |

Approximation Theory | 113 |

Fourier Analysis and Wavelets | 161 |

8 | 170 |

Nonlinear Equations and Their Solution by Iteration 201 | 200 |

Finite Difference Method | 249 |

Sobolev Spaces 273 | 272 |

### Other editions - View all

Theoretical Numerical Analysis: A Functional Analysis Framework Kendall Atkinson,Weimin Han Limited preview - 2007 |

Theoretical Numerical Analysis: A Functional Analysis Framework Kendall Atkinson,Weimin Han Limited preview - 2006 |

Theoretical Numerical Analysis: A Functional Analysis Framework Kendall Atkinson,Weimin Han No preview available - 2008 |

### Common terms and phrases

Assume f assumptions Banach space basis functions bilinear form boundary condition boundary value problem Chapter coefficients compact operator computed consider constant continuous functions convergence convex defined definition denote differential equation Dirichlet discrete Fourier transform discussion eigenvalues elliptic equivalent error bound error estimate Example Exercise exists finite element method fixed point formula Fourier series Fréchet derivative function f Galerkin method Gâteaux given Haar Hilbert space inner product space integral operator interpolation introduce iteration method kernel function Lax-Milgram Lemma linear functional linear operator linear space linear system Lipschitz domain matrix nodes nonlinear normed space obtain orthogonal proof properties Prove quadrature relation result satisfies scaling function Section sequence Show smooth Sobolev spaces subset subspace tion unique solution uniquely solvable variational inequality vector wavelets weak formulation