Contributions To The Theory And Application Of Splines

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The Theory of Splines and Their Applications

Author : J. H. Ahlberg
Publisher : Elsevier
ISBN 13 : 1483222950
Total Pages : 297 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis The Theory of Splines and Their Applications by : J. H. Ahlberg

Download or read book The Theory of Splines and Their Applications written by J. H. Ahlberg and published by Elsevier. This book was released on 2016-06-03 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Theory of Splines and Their Applications discusses spline theory, the theory of cubic splines, polynomial splines of higher degree, generalized splines, doubly cubic splines, and two-dimensional generalized splines. The book explains the equations of the spline, procedures for applications of the spline, convergence properties, equal-interval splines, and special formulas for numerical differentiation or integration. The text explores the intrinsic properties of cubic splines including the Hilbert space interpretation, transformations defined by a mesh, and some connections with space technology concerning the payload of a rocket. The book also discusses the theory of polynomial splines of odd degree which can be approached through algebraically (which depends primarily on the examination in detail of the linear system of equations defining the spline). The theory can also be approached intrinsically (which exploits the consequences of basic integral relations existing between functions and approximating spline functions). The text also considers the second integral relation, raising the order of convergence, and the limits on the order of convergence. The book will prove useful for mathematicians, physicist, engineers, or academicians in the field of technology and applied mathematics.

Splines and PDEs: From Approximation Theory to Numerical Linear Algebra

Author : Angela Kunoth
Publisher : Springer
ISBN 13 : 331994911X
Total Pages : 325 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Splines and PDEs: From Approximation Theory to Numerical Linear Algebra by : Angela Kunoth

Download or read book Splines and PDEs: From Approximation Theory to Numerical Linear Algebra written by Angela Kunoth and published by Springer. This book was released on 2018-09-20 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book takes readers on a multi-perspective tour through state-of-the-art mathematical developments related to the numerical treatment of PDEs based on splines, and in particular isogeometric methods. A wide variety of research topics are covered, ranging from approximation theory to structured numerical linear algebra. More precisely, the book provides (i) a self-contained introduction to B-splines, with special focus on approximation and hierarchical refinement, (ii) a broad survey of numerical schemes for control problems based on B-splines and B-spline-type wavelets, (iii) an exhaustive description of methods for computing and analyzing the spectral distribution of discretization matrices, and (iv) a detailed overview of the mathematical and implementational aspects of isogeometric analysis. The text is the outcome of a C.I.M.E. summer school held in Cetraro (Italy), July 2017, featuring four prominent lecturers with different theoretical and application perspectives. The book may serve both as a reference and an entry point into further research.

Knot Insertion and Deletion Algorithms for B-Spline Curves and Surfaces

Author : Ronald N. Goldman
Publisher : SIAM
ISBN 13 : 0898713064
Total Pages : 204 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Knot Insertion and Deletion Algorithms for B-Spline Curves and Surfaces by : Ronald N. Goldman

Download or read book Knot Insertion and Deletion Algorithms for B-Spline Curves and Surfaces written by Ronald N. Goldman and published by SIAM. This book was released on 1993-01-01 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: New approaches in knot insertion and deletion to understanding, analyzing, and rendering B-spline curves and surfaces.

Handbook of Splines

Author : Gheorghe Micula
Publisher : Springer Science & Business Media
ISBN 13 : 9401153388
Total Pages : 622 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Handbook of Splines by : Gheorghe Micula

Download or read book Handbook of Splines written by Gheorghe Micula and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to give a comprehensive introduction to the theory of spline functions, together with some applications to various fields, emphasizing the significance of the relationship between the general theory and its applications. At the same time, the goal of the book is also to provide new ma terial on spline function theory, as well as a fresh look at old results, being written for people interested in research, as well as for those who are interested in applications. The theory of spline functions and their applications is a relatively recent field of applied mathematics. In the last 50 years, spline function theory has undergone a won derful development with many new directions appearing during this time. This book has its origins in the wish to adequately describe this development from the notion of 'spline' introduced by 1. J. Schoenberg (1901-1990) in 1946, to the newest recent theories of 'spline wavelets' or 'spline fractals'. Isolated facts about the functions now called 'splines' can be found in the papers of L. Euler, A. Lebesgue, G. Birkhoff, J.

Contributions to the Theory and Application of Splines

Author : Knut M. Mørken
Publisher :
ISBN 13 :
Total Pages : 292 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Contributions to the Theory and Application of Splines by : Knut M. Mørken

Download or read book Contributions to the Theory and Application of Splines written by Knut M. Mørken and published by . This book was released on 1989 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Robust Optimization of Spline Models and Complex Regulatory Networks

Author : Ayşe Özmen
Publisher : Springer
ISBN 13 : 3319308009
Total Pages : 143 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Robust Optimization of Spline Models and Complex Regulatory Networks by : Ayşe Özmen

Download or read book Robust Optimization of Spline Models and Complex Regulatory Networks written by Ayşe Özmen and published by Springer. This book was released on 2016-05-11 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces methods of robust optimization in multivariate adaptive regression splines (MARS) and Conic MARS in order to handle uncertainty and non-linearity. The proposed techniques are implemented and explained in two-model regulatory systems that can be found in the financial sector and in the contexts of banking, environmental protection, system biology and medicine. The book provides necessary background information on multi-model regulatory networks, optimization and regression. It presents the theory of and approaches to robust (conic) multivariate adaptive regression splines - R(C)MARS – and robust (conic) generalized partial linear models – R(C)GPLM – under polyhedral uncertainty. Further, it introduces spline regression models for multi-model regulatory networks and interprets (C)MARS results based on different datasets for the implementation. It explains robust optimization in these models in terms of both the theory and methodology. In this context it studies R(C)MARS results with different uncertainty scenarios for a numerical example. Lastly, the book demonstrates the implementation of the method in a number of applications from the financial, energy, and environmental sectors, and provides an outlook on future research.

Spline Functions and the Theory of Wavelets

Author : Serge Dubuc
Publisher : American Mathematical Soc.
ISBN 13 : 0821808753
Total Pages : 409 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Spline Functions and the Theory of Wavelets by : Serge Dubuc

Download or read book Spline Functions and the Theory of Wavelets written by Serge Dubuc and published by American Mathematical Soc.. This book was released on 1999 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is based on a series of thematic workshops on the theory of wavelets and the theory of splines. Important applications are included. The volume is divided into four parts: Spline Functions, Theory of Wavelets, Wavelets in Physics, and Splines and Wavelets in Statistics. Part one presents the broad spectrum of current research in the theory and applications of spline functions. Theory ranges from classical univariate spline approximation to an abstract framework for multivariate spline interpolation. Applications include scattered-data interpolation, differential equations and various techniques in CAGD. Part two considers two developments in subdivision schemes; one for uniform regularity and the other for irregular situations. The latter includes construction of multidimensional wavelet bases and determination of bases with a given time frequency localization. In part three, the multifractal formalism is extended to fractal functions involving oscillating singularites. There is a review of a method of quantization of classical systems based on the theory of coherent states. Wavelets are applied in the domains of atomic, molecular and condensed-matter physics. In part four, ways in which wavelets can be used to solve important function estimation problems in statistics are shown. Different wavelet estimators are proposed in the following distinct cases: functions with discontinuities, errors that are no longer Gaussian, wavelet estimation with robustness, and error distribution that is no longer stationary. Some of the contributions in this volume are current research results not previously available in monograph form. The volume features many applications and interesting new theoretical developments. Readers will find powerful methods for studying irregularities in mathematics, physics, and statistics.

Spline Functions: Basic Theory

Author : Larry Schumaker
Publisher : Cambridge University Press
ISBN 13 : 1139463438
Total Pages : 524 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Spline Functions: Basic Theory by : Larry Schumaker

Download or read book Spline Functions: Basic Theory written by Larry Schumaker and published by Cambridge University Press. This book was released on 2007-08-16 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic work continues to offer a comprehensive treatment of the theory of univariate and tensor-product splines. It will be of interest to researchers and students working in applied analysis, numerical analysis, computer science, and engineering. The material covered provides the reader with the necessary tools for understanding the many applications of splines in such diverse areas as approximation theory, computer-aided geometric design, curve and surface design and fitting, image processing, numerical solution of differential equations, and increasingly in business and the biosciences. This new edition includes a supplement outlining some of the major advances in the theory since 1981, and some 250 new references. It can be used as the main or supplementary text for courses in splines, approximation theory or numerical analysis.

Computation of Curves and Surfaces

Author : Wolfgang Dahmen
Publisher : Springer Science & Business Media
ISBN 13 : 9400920172
Total Pages : 537 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Computation of Curves and Surfaces by : Wolfgang Dahmen

Download or read book Computation of Curves and Surfaces written by Wolfgang Dahmen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assembled here is a collection of articles presented at a NATO ADVANCED STU DY INSTITUTE held at Puerto de la Cruz, Tenerife, Spain during the period of July 10th to 21st, 1989. In addition to the editors of these proceedings Professor Larry L. Schumaker from Vanderbilt University, Nashville, Tennessee, served as a member of the international organizing committee. The contents of the contribu tions fall within the heading of COMPUTATION OF CURVES AND SURFACES and therefore address mathematical and computational issues pertaining to the dis play, modeling, interrogation and representation of complex geometrical objects in various scientific and technical environments. As is the intent of the NATO ASI program the meeting was two weeks in length and the body of the scientific activities was organized around prominent experts. Each of them presented lectures on his current research activity. We were fortunate to have sixteen distinguished invited speakers representing nine NATO countries: W. Bohm (Federal Republic of Germany), C. de Boor (USA), C.K. Chui (USA), W. Dahmen (Federal Republic of Germany), F. Fontanella (Italy), M. Gasca (Spain), R. Goldman (Canada), T.N.T. Goodman (UK), J.A. Gregory (UK), C. Hoffman (USA), J. Hoschek (Federal Republic of Germany), A. Le Mehaute (France), T. Lyche (Norway), C.A. Micchelli (USA), 1.1. Schumaker (USA), C. Traas (The Netherlands). The audience consisted of both young researchers as well as established scientists from twelve NATO countries and several non-NATO countries.

Approximation and Modeling with B-Splines

Author : Klaus Hollig
Publisher : SIAM
ISBN 13 : 1611972949
Total Pages : 228 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Approximation and Modeling with B-Splines by : Klaus Hollig

Download or read book Approximation and Modeling with B-Splines written by Klaus Hollig and published by SIAM. This book was released on 2015-07-01 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: B-splines are fundamental to approximation and data fitting, geometric modeling, automated manufacturing, computer graphics, and numerical simulation. With an emphasis on key results and methods that are most widely used in practice, this textbook provides a unified introduction to the basic components of B-spline theory: approximation methods (mathematics), modeling techniques (engineering), and geometric algorithms (computer science). A supplemental Web site will provide a collection of problems, some with solutions, slides for use in lectures, and programs with demos.

Theory and Applications of Spline Functions

Author : Thomas Nall Eden Greville
Publisher :
ISBN 13 :
Total Pages : 232 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Theory and Applications of Spline Functions by : Thomas Nall Eden Greville

Download or read book Theory and Applications of Spline Functions written by Thomas Nall Eden Greville and published by . This book was released on 1969 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonparametric Functional Estimation

Author : B. L. S. Prakasa Rao
Publisher : Academic Press
ISBN 13 : 148326923X
Total Pages : 539 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Nonparametric Functional Estimation by : B. L. S. Prakasa Rao

Download or read book Nonparametric Functional Estimation written by B. L. S. Prakasa Rao and published by Academic Press. This book was released on 2014-07-10 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonparametric Functional Estimation is a compendium of papers, written by experts, in the area of nonparametric functional estimation. This book attempts to be exhaustive in nature and is written both for specialists in the area as well as for students of statistics taking courses at the postgraduate level. The main emphasis throughout the book is on the discussion of several methods of estimation and on the study of their large sample properties. Chapters are devoted to topics on estimation of density and related functions, the application of density estimation to classification problems, and the different facets of estimation of distribution functions. Statisticians and students of statistics and engineering will find the text very useful.

Control Theoretic Splines

Author : Magnus Egerstedt
Publisher : Princeton University Press
ISBN 13 : 1400833876
Total Pages : 232 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Control Theoretic Splines by : Magnus Egerstedt

Download or read book Control Theoretic Splines written by Magnus Egerstedt and published by Princeton University Press. This book was released on 2009-12-07 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Uneasy Alliance

Author : Jagdish Chandra
Publisher : SIAM
ISBN 13 : 0898715350
Total Pages : 104 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis An Uneasy Alliance by : Jagdish Chandra

Download or read book An Uneasy Alliance written by Jagdish Chandra and published by SIAM. This book was released on 2005-01-01 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the complex and challenging organizational and scientific issues that arose in the operation of the MRC.

Cardinal Spline Interpolation

Author : I. J. Schoenberg
Publisher : SIAM
ISBN 13 : 089871009X
Total Pages : 127 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Cardinal Spline Interpolation by : I. J. Schoenberg

Download or read book Cardinal Spline Interpolation written by I. J. Schoenberg and published by SIAM. This book was released on 1973-01-01 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the author explains cardinal spline functions, the basic properties of B-splines and exponential Euler splines.

Approximation Theory

Author : Z. Ciesielski
Publisher : Springer Science & Business Media
ISBN 13 : 9789027704832
Total Pages : 312 pages
Book Rating : 4.7/5 (48 download)

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Book Synopsis Approximation Theory by : Z. Ciesielski

Download or read book Approximation Theory written by Z. Ciesielski and published by Springer Science & Business Media. This book was released on 1975-05-31 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the Conference jointly organized by the Mathematical Institute of the Polish Academy of Science and the Institute of Adam Mickiewicz University, held in Poznan, 22-26 August 1972

Splines And Compartment Models: An Introduction

Author : Karl-ernst Erich Biebler
Publisher : World Scientific
ISBN 13 : 9814522244
Total Pages : 349 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Splines And Compartment Models: An Introduction by : Karl-ernst Erich Biebler

Download or read book Splines And Compartment Models: An Introduction written by Karl-ernst Erich Biebler and published by World Scientific. This book was released on 2013-07-23 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents methods of mathematical modeling from two points of view. Splines provide a general approach while compartment models serve as examples for context related to modeling. The preconditions and characteristics of the developed mathematical models as well as the conditions surrounding data collection and model fit are taken into account. The substantial statements of this book are mathematically proven. The results are ready for application with examples and related program codes given.In this book, splines are algebraically developed such that the reader or user can easily understand and vary the numerical construction of the different kinds of spline functions. The classical compartment models of the pharmacokinetics are systematically analyzed and connected with lifetime distributions. As such, parameter estimation and model fit can be treated statistically with a varied minimum chi-square method. This method is applicable for single kinetics and also allows the calculation of average kinetics.