Topics In Splines And Applications

Author : Young Kinh-Nhue Truong,Muhammad Sarfraz
Publisher : BoD – Books on Demand
Page : 162 pages
File Size : 49,6 Mb
Release : 2018-06-06
Category : Computers
ISBN : 9781789232509

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Topics in Splines and Applications by Young Kinh-Nhue Truong,Muhammad Sarfraz Pdf

Splines provide a significant tool for the design of computationally economical curves and surfaces for the construction of various objects like automobiles, ship hulls, airplane fuselages and wings, propeller blades, shoe insoles, bottles, etc. It also contributes in the description of geological, physical, statistical, and even medical phenomena. Spline methods have proven to be indispensable in a variety of modern industries, including computer vision, robotics, signal and image processing, visualization, textile, graphic designs, and even media. This book aims to provide a valuable source on splines and their applications. It focuses on collecting and disseminating information in various disciplines including computer-aided geometric design, computer graphics, data visualization, data fitting, power systems, clinical and epidemiologic studies, disease detection, regression curves, social media, and biological studies. The book is useful for researchers, scientists, practitioners, and many others who seek state-of-the-art techniques and applications using splines. It is also useful for undergraduate senior students as well as graduate students in the areas of computer science, engineering, health science, statistics, and mathematics. Each chapter also provides useful information on software developments and their extensions.

Author : Muhammad Sarfraz,Young Kinh-Nhue Truong
Publisher : Unknown
Page : 160 pages
File Size : 47,9 Mb
Release : 2018
Category : Mathematics
ISBN : 1789232511

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Topics in Splines and Applications by Muhammad Sarfraz,Young Kinh-Nhue Truong Pdf

Splines provide a significant tool for the design of computationally economical curves and surfaces for the construction of various objects like automobiles, ship hulls, airplane fuselages and wings, propeller blades, shoe insoles, bottles, etc. It also contributes in the description of geological, physical, statistical, and even medical phenomena. Spline methods have proven to be indispensable in a variety of modern industries, including computer vision, robotics, signal and image processing, visualization, textile, graphic designs, and even media. This book aims to provide a valuable source on splines and their applications. It focuses on collecting and disseminating information in various disciplines including computer-aided geometric design, computer graphics, data visualization, data fitting, power systems, clinical and epidemiologic studies, disease detection, regression curves, social media, and biological studies. The book is useful for researchers, scientists, practitioners, and many others who seek state-of-the-art techniques and applications using splines. It is also useful for undergraduate senior students as well as graduate students in the areas of computer science, engineering, health science, statistics, and mathematics. Each chapter also provides useful information on software developments and their extensions.

Author : J. H. Ahlberg,E. N. Nilson,J. L. Walsh
Publisher : Elsevier
Page : 296 pages
File Size : 51,9 Mb
Release : 2016-06-03
Category : Mathematics
ISBN : 9781483222950

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The Theory of Splines and Their Applications by J. H. Ahlberg,E. N. Nilson,J. L. Walsh Pdf

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.

Author : Gary D. Knott
Publisher : Springer Science & Business Media
Page : 247 pages
File Size : 49,8 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9781461213208

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Interpolating Cubic Splines by Gary D. Knott Pdf

A spline is a thin flexible strip composed of a material such as bamboo or steel that can be bent to pass through or near given points in the plane, or in 3-space in a smooth manner. Mechanical engineers and drafting specialists find such (physical) splines useful in designing and in drawing plans for a wide variety of objects, such as for hulls of boats or for the bodies of automobiles where smooth curves need to be specified. These days, physi cal splines are largely replaced by computer software that can compute the desired curves (with appropriate encouragment). The same mathematical ideas used for computing "spline" curves can be extended to allow us to compute "spline" surfaces. The application ofthese mathematical ideas is rather widespread. Spline functions are central to computer graphics disciplines. Spline curves and surfaces are used in computer graphics renderings for both real and imagi nary objects. Computer-aided-design (CAD) systems depend on algorithms for computing spline functions, and splines are used in numerical analysis and statistics. Thus the construction of movies and computer games trav els side-by-side with the art of automobile design, sail construction, and architecture; and statisticians and applied mathematicians use splines as everyday computational tools, often divorced from graphic images.

Author : Amir Z. Averbuch,Pekka Neittaanmäki,Valery A. Zheludev
Publisher : Springer
Page : 287 pages
File Size : 40,9 Mb
Release : 2018-06-19
Category : Technology & Engineering
ISBN : 9783319921235

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Spline and Spline Wavelet Methods with Applications to Signal and Image Processing by Amir Z. Averbuch,Pekka Neittaanmäki,Valery A. Zheludev Pdf

This book provides a practical guide, complete with accompanying Matlab software, to many different types of polynomial and discrete splines and spline-based wavelets, multiwavelets and wavelet frames in signal and image processing applications. In self-contained form, it briefly outlines a broad range of polynomial and discrete splines with equidistant nodes and their signal-processing-relevant properties. In particular, interpolating, smoothing, and shift-orthogonal splines are presented.

Author : Klaus Hollig,Jorg Horner
Publisher : SIAM
Page : 228 pages
File Size : 48,8 Mb
Release : 2015-07-01
Category : Mathematics
ISBN : 9781611972948

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Approximation and Modeling with B-Splines by Klaus Hollig,Jorg Horner Pdf

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.

Author : Yuedong Wang
Publisher : CRC Press
Page : 380 pages
File Size : 52,8 Mb
Release : 2011-06-22
Category : Computers
ISBN : 9781420077568

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Smoothing Splines by Yuedong Wang Pdf

A general class of powerful and flexible modeling techniques, spline smoothing has attracted a great deal of research attention in recent years and has been widely used in many application areas, from medicine to economics. Smoothing Splines: Methods and Applications covers basic smoothing spline models, including polynomial, periodic, spherical, t

Author : Chong Gu
Publisher : Springer Science & Business Media
Page : 446 pages
File Size : 41,6 Mb
Release : 2013-01-26
Category : Mathematics
ISBN : 9781461453697

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Smoothing Spline ANOVA Models by Chong Gu Pdf

Nonparametric function estimation with stochastic data, otherwise known as smoothing, has been studied by several generations of statisticians. Assisted by the ample computing power in today's servers, desktops, and laptops, smoothing methods have been finding their ways into everyday data analysis by practitioners. While scores of methods have proved successful for univariate smoothing, ones practical in multivariate settings number far less. Smoothing spline ANOVA models are a versatile family of smoothing methods derived through roughness penalties, that are suitable for both univariate and multivariate problems. In this book, the author presents a treatise on penalty smoothing under a unified framework. Methods are developed for (i) regression with Gaussian and non-Gaussian responses as well as with censored lifetime data; (ii) density and conditional density estimation under a variety of sampling schemes; and (iii) hazard rate estimation with censored life time data and covariates. The unifying themes are the general penalized likelihood method and the construction of multivariate models with built-in ANOVA decompositions. Extensive discussions are devoted to model construction, smoothing parameter selection, computation, and asymptotic convergence. Most of the computational and data analytical tools discussed in the book are implemented in R, an open-source platform for statistical computing and graphics. Suites of functions are embodied in the R package gss, and are illustrated throughout the book using simulated and real data examples. This monograph will be useful as a reference work for researchers in theoretical and applied statistics as well as for those in other related disciplines. It can also be used as a text for graduate level courses on the subject. Most of the materials are accessible to a second year graduate student with a good training in calculus and linear algebra and working knowledge in basic statistical inferences such as linear models and maximum likelihood estimates.

Author : Charles K. Chui
Publisher : SIAM
Page : 192 pages
File Size : 54,5 Mb
Release : 1988-01-01
Category : Mathematics
ISBN : 9780898712261

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Multivariate Splines by Charles K. Chui Pdf

Subject of multivariate splines presented from an elementary point of view; includes many open problems.

Author : Gheorghe Micula,Sanda Micula
Publisher : Springer Science & Business Media
Page : 622 pages
File Size : 52,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401153386

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Handbook of Splines by Gheorghe Micula,Sanda Micula Pdf

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.

Author : S.P. Singh
Publisher : Springer Science & Business Media
Page : 482 pages
File Size : 41,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401126342

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Approximation Theory, Spline Functions and Applications by S.P. Singh Pdf

These are the Proceedings of the NATO Advanced Study Institute on Approximation Theory, Spline Functions and Applications held in the Hotel villa del Mare, Maratea, Italy between April 28,1991 and May 9, 1991. The principal aim of the Advanced Study Institute, as reflected in these Proceedings, was to bring together recent and up-to-date developments of the subject, and to give directions for future research. Amongst the main topics covered during this Advanced Study Institute is the subject of uni variate and multivariate wavelet decomposition over spline spaces. This is a relatively new area in approximation theory and an increasingly impor tant subject. The work involves key techniques in approximation theory cardinal splines, B-splines, Euler-Frobenius polynomials, spline spaces with non-uniform knot sequences. A number of scientific applications are also highlighted, most notably applications to signal processing and digital im age processing. Developments in the area of approximation of functions examined in the course of our discussions include approximation of periodic phenomena over irregular node distributions, scattered data interpolation, Pade approximants in one and several variables, approximation properties of weighted Chebyshev polynomials, minimax approximations, and the Strang Fix conditions and their relation to radial functions. I express my sincere thanks to the members of the Advisory Commit tee, Professors B. Beauzamy, E. W. Cheney, J. Meinguet, D. Roux, and G. M. Phillips. My sincere appreciation and thanks go to A. Carbone, E. DePas cale, R. Charron, and B.

Author : John H. Ahlberg,Edwin N. Nilson,Joseph L. Walsh
Publisher : Unknown
Page : 284 pages
File Size : 51,5 Mb
Release : 1982
Category : Electronic
ISBN : OCLC:633220473

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The theory of splines and their applications by John H. Ahlberg,Edwin N. Nilson,Joseph L. Walsh Pdf

Author : Ren-Hong Wang
Publisher : Springer Science & Business Media
Page : 522 pages
File Size : 55,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401723787

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Multivariate Spline Functions and Their Applications by Ren-Hong Wang Pdf

This book deals with the algebraic geometric method of studying multivariate splines. Topics treated include: the theory of multivariate spline spaces, higher-dimensional splines, rational splines, piecewise algebraic variety (including piecewise algebraic curves and surfaces) and applications in the finite element method and computer-aided geometric design. Many new results are given. Audience: This volume will be of interest to researchers and graduate students whose work involves approximations and expansions, numerical analysis, computational geometry, image processing and CAD/CAM.

Author : I. J. Schoenberg
Publisher : SIAM
Page : 131 pages
File Size : 40,9 Mb
Release : 1973-01-01
Category : Mathematics
ISBN : 1611970555

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Cardinal Spline Interpolation by I. J. Schoenberg Pdf

As this monograph shows, the purpose of cardinal spline interpolation is to bridge the gap between the linear spline and the cardinal series. The author explains cardinal spline functions, the basic properties of B-splines, including B- splines with equidistant knots and cardinal splines represented in terms of B-splines, and exponential Euler splines, leading to the most important case and central problem of the book-- cardinal spline interpolation, with main results, proofs, and some applications. Other topics discussed include cardinal Hermite interpolation, semi-cardinal interpolation, finite spline interpolation problems, extremum and limit properties, equidistant spline interpolation applied to approximations of Fourier transforms, and the smoothing of histograms.

Author : Borislav D. Bojanov,H. Hakopian,B. Sahakian
Publisher : Springer Science & Business Media
Page : 287 pages
File Size : 45,8 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401581691

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Spline Functions and Multivariate Interpolations by Borislav D. Bojanov,H. Hakopian,B. Sahakian Pdf

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 to introduce the reader to the theory of spline functions. The emphasis is given to some new developments, such as the general Birkoff's type interpolation, the extremal properties of the splines and their prominant role in the optimal recovery of functions, multivariate interpolation by polynomials and splines. The material presented is based on the lectures of the authors, given to the students at the University of Sofia and Yerevan University during the last 10 years. Some more elementary results are left as excercises and detailed hints are given.