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Curve and surface fitting with splines
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ISBN: 019853440X Year: 1996 Publisher: Oxford Clarendon


Book
Control theoretic splines : optimal control, statistics, and path planning
Authors: --- ---
ISBN: 1282457969 1282936069 9786612936067 9786612457968 1400833876 9781400833870 9781282457966 6612457961 9780691132969 0691132968 Year: 2010 Publisher: Princeton : Princeton University Press,

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Abstract

Splines, both interpolatory and smoothing, have a long and rich history that has largely been application driven. This book unifies these constructions in a comprehensive and accessible way, drawing from the latest methods and applications to show how they arise naturally in the theory of linear control systems. Magnus Egerstedt and Clyde Martin are leading innovators in the use of control theoretic splines to bring together many diverse applications within a common framework. In this book, they begin with a series of problems ranging from path planning to statistics to approximation. Using the tools of optimization over vector spaces, Egerstedt and Martin demonstrate how all of these problems are part of the same general mathematical framework, and how they are all, to a certain degree, a consequence of the optimization problem of finding the shortest distance from a point to an affine subspace in a Hilbert space. They cover periodic splines, monotone splines, and splines with inequality constraints, and explain how any finite number of linear constraints can be added. This book reveals how the many natural connections between control theory, numerical analysis, and statistics can be used to generate powerful mathematical and analytical tools. This book is an excellent resource for students and professionals in control theory, robotics, engineering, computer graphics, econometrics, and any area that requires the construction of curves based on sets of raw data.

Smoothing techniques for curve estimation
Authors: ---
ISBN: 0387097066 0387097074 3540097066 3540384758 Year: 1979 Volume: 757 Publisher: Berlin : Springer,

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This work introduces new developments in the construction, analysis, and implementation of parallel computing algorithms. This book presents 23 self-contained chapters, including surveys, written by distinguished researchers in the field of parallel computing. Each chapter is devoted to some aspects of the subject: parallel algorithms for matrix computations, parallel optimization, management of parallel programming models and data, with the largest focus on parallel scientific computing in industrial applications.Key features include: construction and analysis of parallel algorithms for linear algebra and optimization problems; different aspects of parallel architectures, including distributed memory computers with multicore processors; a wide range of industrial applications: parallel simulation of flows through oil filters as well as in porous and gas media, jet aerodynamics, heat conduction in electrical cables, nonlinear optics processes in tapered lasers, and molecular and cell dynamics.


Book
Least squares data fitting with applications
Authors: --- --- ---
ISBN: 1421408589 9781421408583 1421407868 9781421407869 Year: 2013 Publisher: Baltimore, Md. : Johns Hopkins University Press,

Fitting models to biological data using linear and nonlinear regression : a practical guide to curve fitting
Authors: --- ---
ISBN: 9780198038344 0198038348 9786610843770 6610843775 1280843772 9781280843778 0195171802 0195171799 9780195171792 9780195171808 Year: 2004 Publisher: Oxford ; New York : Oxford University Press,

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Most biologists use nonlinear regression more than any other statistical technique, but there are very few places to learn about curve-fitting. This book addresses this relatively focused need of an extraordinarily broad range of scientists.


Book
Ausgleichungsrechnung : Statistische Auswertemethoden
Authors: ---
ISBN: 1283428601 9786613428608 3110206781 Year: 2008 Publisher: Berlin ; Boston : De Gruyter,


Book
Curve and surface fitting with splines
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ISBN: 0198534418 Year: 1993 Volume: *1 Publisher: Oxford Clarendon

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Fitting equations to data : computer analysis of multifactor data
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ISBN: 0471053708 Year: 1980 Publisher: New York (N.Y.): Wiley


Book
From Curve Fitting to Machine Learning : An Illustrative Guide to Scientific Data Analysis and Computational Intelligence
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ISBN: 3642212794 3642212808 Year: 2011 Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer,

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The analysis of experimental data is at heart of science from its beginnings. But it was the advent of digital computers that allowed the execution of highly non-linear and increasingly complex data analysis procedures - methods that were completely unfeasible before. Non-linear curve fitting, clustering and machine learning belong to these modern techniques which are a further step towards computational intelligence. The goal of this book is to provide an interactive and illustrative guide to these topics. It concentrates on the road from two dimensional curve fitting to multidimensional clustering and machine learning with neural networks or support vector machines. Along the way topics like mathematical optimization or evolutionary algorithms are touched. All concepts and ideas are outlined in a clear cut manner with graphically depicted plausibility arguments and a little elementary mathematics. The major topics are extensively outlined with exploratory examples and applications. The primary goal is to be as illustrative as possible without hiding problems and pitfalls but to address them. The character of an illustrative cookbook is complemented with specific sections that address more fundamental questions like the relation between machine learning and human intelligence All topics are completely demonstrated with the aid of the commercial computing platform Mathematica and the Computational Intelligence Packages (CIP), a high-level function library developed with Mathematica's programming language on top of Mathematica's algorithms. CIP is open-source so the detailed code of every method is freely accessible. All examples and applications shown throughout the book may be used and customized by the reader without any restrictions.

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