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Spline Functions and Multivariate Interpolations
Spline functions entered Approximation Theory as solutions of natural extremal problems. A typical example is the problem of drawing a function curve through given n + k points that has a minimal norm of its k-th derivative. Isolated facts about the functions, now called splines, can be found in the papers of L. Euler, A. Lebesgue, G. Birkhoff, J. Favard, L. Tschakaloff. However, the Theory of Spline Functions has developed in the last 30 years by the effort of dozens of mathematicians. Recent fundamental results on multivariate polynomial interpolation and multivari ate splines have initiated a new wave of theoretical investigations and variety of applications. The purpose of this book is t...
Advanced Topics In Multivariate Approximation - Proceedings Of The International Workshop
This volume consists of 24 refereed carefully edited papers on various topics in multivariate approximation. It represents the proceedings of a workshop organized by the University of Firenze, and held in September 1995 in Montecatini, Italy.The main themes of the volume are multiresolution analysis and wavelets, multidimensional interpolation and smoothing, and computer-aided geometric design. A number of particular topics are included, like subdivision algorithms, constrained approximation and shape-preserving algorithms, thin plate splines, radial basis functions, treatment of scattered data, rational surfaces and offsets, blossoming, grid generation, surface reconstruction, algebraic curves and surfaces, and neural networks.
Splinefunktionen
Der Begriff der Splinefunktionen wurde von I.J. Schoenberg 1946 eingefUhrt. "Spline" ist der Name eines Zeichengerates, welches auf mechanischem Weg Interpolatio- aufgaben lost. Dieses Gerat besteht aus einer flexiblen, oft mehrere Meter langen Latte, die auf dem Zeichenbrett aufliegt und dort an bestimmten Stellen durch Gewichte festgehalten wird. Die Form, die die Latte annimmt, hangt von den Elastizitatseigenschaften der Latte abo -, ", \, \ \ I, "--"', J::>--", I I, I I I, ") Fig. 1: Latteninterpo1ation Po1ynominterpo1ation _ - - - - - - - --0 Wir konnen natUrlich versuchen, ein mathematisches Modell fUr dieses mechanische Zeichengerat zu machen, d. h. die Gestalt solcher Kurven mathemat...
The Caucasian Knot
As the Soviet Union entered its death throes, the self-determination of the nations within its republics became an issue over which people were prepared to die. When Azerbaijan declared its independence, the Armenian enclave of Nagorno-Karabagh followed suit. Before long, pogrom and war were the order of the day, resulting in thousands of Armenian and Azeri casualties. This book examines the history of Mountainous Karabagh, the ancient Artsakh of the Armenians, and assesses the mass of archaeological material and documentary evidence supporting the conflicting Azeri and Armenian claims. The authors follow the populations of the area from antiquity through periods of Mongol, Turkmen and Persi...
Iaeng Transactions On Engineering Sciences: Special Issue For The International Association Of Engineers Conferences 2014
Two large international conferences on Advances in Engineering Sciences were held in Hong Kong, March 12-14, 2014, under the International MultiConference of Engineers and Computer Scientists (IMECS 2014), and in London, UK, 2-4 July, 2014, under the World Congress on Engineering 2014 (WCE 2014) respectively. This volume contains 37 revised and extended research articles written by prominent researchers participating in the conferences. Topics covered include engineering mathematics, computer science, electrical engineering, manufacturing engineering, industrial engineering, and industrial applications. The book offers tremendous state-of-the-art advances in engineering sciences and also serves as an excellent reference work for researchers and graduate students working with/on engineering sciences.
Hidden Histories
Tuscany is a landscape whose cultural construction is complicated and multi-layered. It is this very complexity that this book seeks to untangle. By revealing hidden histories, we learn how food, landscape and architecture are intertwined, as well as the extent to which Italian design and contemporary consumption patterns form a legacy that draws upon the Romantic longings of a century before. In the process, this book reveals the extent to which Tuscany has been constructed by Anglos — and what has been distorted, idealized and even overlooked in the process.
Multivariate Approximation Theory III
The Fourth International Symposium on Multivariate Approximation Theory was held at the Oberwolfach Mathematical Research Insti tute, Black Forest, W.-Germany, during the week of January 20 - 26, 1985. The preceding conferences on this topic were held in 1976, 1979, and 1982 * . We were pleased to have more than 50 mathematicians from 13 countries in attendance. The program in cluded 40 lectures. These Proceedings form a record of most of the papers presented at the Symposium. The topics treated cover different problems on multivariate approximation such as polynomial approximation on simplices, multivariate splines (box-splines, dimension of spline spaces), blending methods, multivariate He...
Approximation Theory
"Contains the contributions of 45 internationally distinguished mathematicians covering all areas of approximation theory-written in honor of the pioneering work of Arun K. Varma to the fields of interpolation and approximation of functions, including Birhoff interpolation and approximation by spline functions."
Approximate Approximations
In this book, a new approach to approximation procedures is developed. This new approach is characterized by the common feature that the procedures are accurate without being convergent as the mesh size tends to zero. This lack of convergence is compensated for by the flexibility in the choice of approximating functions, the simplicity of multi-dimensional generalizations, and the possibility of obtaining explicit formulas for the values of various integral and pseudodifferential operators applied to approximating functions. The developed techniques allow the authors to design new classes of high-order quadrature formulas for integral and pseudodifferential operators, to introduce the concept of approximate wavelets, and to develop new efficient numerical and semi-numerical methods for solving boundary value problems of mathematical physics. The book is intended for researchers interested in approximation theory and numerical methods for partial differential and integral equations.
Dynamic Stochastic Optimization
Uncertainties and changes are pervasive characteristics of modern systems involving interactions between humans, economics, nature and technology. These systems are often too complex to allow for precise evaluations and, as a result, the lack of proper management (control) may create significant risks. In order to develop robust strategies we need approaches which explic itly deal with uncertainties, risks and changing conditions. One rather general approach is to characterize (explicitly or implicitly) uncertainties by objec tive or subjective probabilities (measures of confidence or belief). This leads us to stochastic optimization problems which can rarely be solved by using the standard ...
