Multidimensional minimizing splines : theory and applications

This 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). Contents......Page 6 Preface......Page 10 Preliminaries......Page 14 Part A. (m,s)-Splines......Page 18 Introduction......Page 20 1. Definition......Page 22 2. Imbeddings and norms......Page 24 1. Definition and first properties......Page 30 2. The space of (m,s)-spline functions. Examples......Page 32 3. Other problems. Splines defined by local mean values......Page 39 4. Computation of interpolating splines......Page 42 5. A convergence result......Page 44 6. Auxiliary results......Page 48 7. Estimates of the approximation error......Page 52 1. Definition and first properties......Page 56 2. Computation of smoothing splines......Page 57 3. Convergence results......Page 59 4. Estimates of the approximation error......Page 63 5. Convergence for noisy data......Page 67 1. The spaces X[sup(m,l,s)]......Page 70 2. Interpolating (m,l,s)-splines......Page 71 3. Smoothing (m,l,s)-splines......Page 72 Part B. D[sup(m)]-Splines over a Bounded Domain of R[sup(n)]......Page 74 Introduction......Page 76 1. Interpolating D[sup(m)]-splines......Page 78 2. The space of D[sup(m)]-splines......Page 81 3. Smoothing D[sup(m)]-splines......Page 82 4. Convergence and error estimates......Page 83 1. The finite element framework......Page 86 2. Discrete interpolating D[sup(m)]-splines......Page 89 3. Discrete smoothing D[sup(m)]-splines......Page 97 1. Characterization and explicit form......Page 106 2. Computation of D[sup(m)]-splines......Page 110 3. Cubic splines......Page 112 4. Tensor product of univariate D[sup(m)]-splines......Page 116 Part C. Applications of Discrete D[sup(m)]-splines......Page 118 Introduction......Page 120 2. The fitting method......Page 122 3. Examples of finite elements......Page 124 5. An interpolation-smoothing mixed method......Page 127 6. Numerical results......Page 130 1. Formulation of the problem......Page 148 2. Spaces of functions on Ω'......Page 150 3. D[sup(m)]-splines over Ω'......Page 153 4. Discrete D[sup(m)]-splines......Page 157 5. Global convergence......Page 162 6. Local convergence......Page 165 7. Approximation of explicit surfaces with vertical faults......Page 174 8. Numerical results......Page 177 1. Formulation of the problem......Page 192 2. Approximation of [Equation Omitted]......Page 194 3. Spline fitting......Page 196 4. Convergence of the approximation......Page 200 5. Numerical results......Page 205 2. Spline fitting......Page 216 3. Convergence of the approximation......Page 221 4. Numerical results......Page 225 1. Introduction......Page 236 2. Formulation of the problem......Page 237 3. Spline fitting......Page 239 4. Convergence of the approximation......Page 242 5. Numerical results......Page 244 Bibliography......Page 264 D......Page 274 G......Page 275 P......Page 276 T......Page 277 Z......Page 278 Audience: This book would be 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 "This book is meant for mathematicians, geologists, engineers and, in general, researchers and postgraduate students involved in spline function theory, surface fitting problems or variational methods."--BOOK JACKET.