## Multidimensional Minimizing Splines: Theory and ApplicationsThis book is of interest to mathematicians, geologists, engineers and, in general, researchers and post graduate students involved in spline function theory, surface fitting problems or variational methods. From reviews: The book is well organized, and the English is very good. I recommend the book to researchers in approximation theory, and to anyone interested in bivariate data fitting." (L.L. Schumaker, Mathematical Reviews, 2005). |

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### Contents

Smoothing Part B over a Bounded Domain of Introduction V over 55 | 4 |

The space of functions Examples | 15 |

Other problems Splines defined by local mean values | 22 |

Auxiliary results | 31 |

Convergence for noisy data IV 1 2 The spaces Interpolating | 50 |

Interpolating | 61 |

Tensor product of univariate Part C Applications of Discrete | 99 |

Construction of explicit surfaces from large data sets | 105 |

IX | 130 |

X | 175 |

XI | 199 |

247 | |

255 | |

257 | |

### Other editions - View all

Multidimensional Minimizing Splines: Theory and Applications R. Arcangéli,María Cruz López de Silanes,Juan José Torrens No preview available - 2013 |

Multidimensional Minimizing Splines: Theory and Applications R. Arcangéli,María Cruz López de Silanes,Juan José Torrens No preview available - 2013 |

### Common terms and phrases

approximation Arcangéli assume basis functions bounded open Cauchy sequence Chapter coefficients computation condition consider constants introduced contains a subset convergence result Corollary I–2.1 data points deduce definition derivatives of order dimension discontinuity set discrete smoothing distribution Duchon error estimates Euclidean distance example exists a constant finite element space following result function defined given Hausdorff distance Hence Hilbert space holds hypothesis implies integer interpolating relative interpolating spline Lagrange Lax-Milgram Lemma Lemma Let us observe Let us prove Likewise linear system Lipschitz-continuous boundary cf locally integrable function López de Silanes M. C. López mapping matrix notations null obtain open set open subset operator defined P. G. Ciarlet 45 polygonal Preliminaries problem 1.1 proof of Theorem Proposition 2.2 real number Remark resp satisfied scalar product Schwartz 131 semi-Hilbert space semi-norm Silanes smoothing relative Sobolev space subspace Suppose that II–5.1 surface taking into account Theorem 2.1 thin plate splines triangulation unique solution values vector