Download or read book Discrete polynomial spline approximation methods written by Tom Johan Wiborg Lyche and published by . This book was released on 1975 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Convergence of Discrete Cubic Quartic and Quintic Splines written by Yadvendra Prasad Dubey and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Methods of Shape preserving Spline Approximation written by Boris I. Kvasov and published by World Scientific. This book was released on 2000 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to develop algorithms of shape-preserving spline approximation for curves/surfaces with automatic choice of the tension parameters. The resulting curves/surfaces retain geometric properties of the initial data, such as positivity, monotonicity, convexity, linear and planar sections. The main tools used are generalized tension splines and B-splines. A difference method for constructing tension splines is also developed which permits one to avoid the computation of hyperbolic functions and provides other computational advantages. The algorithms of monotonizing parametrization described improve an adequate representation of the resulting shape-preserving curves/surfaces. Detailed descriptions of algorithms are given, with a strong emphasis on their computer implementation. These algorithms can be applied to solve many problems in computer-aided geometric design.
Download or read book Constructive Aspects of Discrete Polynomial Spline Functions written by Larry L. Schumaker and published by . This book was released on 1973 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Interpolation by Higher Degree Discrete Spline written by Yadvendra Prasad Dubey and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Discrete Polynomial Splines written by and published by . This book was released on 1989 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spline and Spline Wavelet Methods with Applications to Signal and Image Processing written by Amir Z. Averbuch and published by Springer. This book was released on 2018-06-19 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Download or read book Divided Differences Falling Factorials and Discrete Splines written by Ryan J. Tibshirani and published by . This book was released on 2022-07-21 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph reviews a class of univariate piecewise polynomial functions known as discrete splines, which share properties analogous to the better-known class of spline functions, but where continuity in derivatives is replaced by continuity in divided differences. As it happens, discrete splines bear connections to a wide array of developments in applied mathematics and statistics, from divided differences and Newton interpolation, dating back 300 years, to the recent emergence of trend filtering. In this concise yet comprehensive monograph, the author uses his recognized expertise on the subject to guide the reader through these connections. In doing so, the author provides an insightful journey through the historical and most recent developments, contributing some new perspectives and results along the way. Written for researchers and advanced level students of applied mathematics and statistics, this monograph will be of particular interest to those using trend filtering in machine learning applications.
Download or read book Splines and Variational Methods written by P. M. Prenter and published by Courier Corporation. This book was released on 2008-01-01 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the clearest available introductions to variational methods, this text requires only a minimal background in linear algebra and analysis. It explains the application of theoretic notions to the kinds of physical problems that engineers regularly encounter. Many helpful definitions, examples, and exercises appear throughout the book. 1975 edition.
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.
Download or read book Vertex Splines and Their Applications to Interpolation of Discrete Data written by C. K. Chui and published by . This book was released on 1989 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is well known that B-splines in one variable play a central role in the theory of spline functions. However, although there are various generalizations of the notion of B-splines to the multi-variable setting in the literature, very little is known at this writing on the structure and theory of all compactly supported smooth piecewise polynomial functions on a preassigned grid partition \Delta in R^s , s > 1, unless \Delta is perfectly regular. While we don't have much to offer to the general theory, we will be satisfied with the study of those compactly supported ones with each support containing at least one common vertex and with the interior of the support containing at most one vertex of \Delta. These functions are called vertex splines. The objective of this presentation is to give a brief description of the notion of vertex splines and to discuss their applications to interpolation of discrete data with or without constraints.
Download or read book Polynomial and Spline Approximation written by B.N. Sahney and published by Springer. This book was released on 1979-05-31 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Study Institute, Calgary, Canada, August 26-September 2, 1978
Download or read book Box Splines written by Carl de Boor and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Compactly supported smooth piecewise polynomial functions provide an efficient tool for the approximation of curves and surfaces and other smooth functions of one and several arguments. Since they are locally polynomial, they are easy to evaluate. Since they are smooth, they can be used when smoothness is required, as in the numerical solution of partial differential equations (in the Finite Element method) or the modeling of smooth sur faces (in Computer Aided Geometric Design). Since they are compactly supported, their linear span has the needed flexibility to approximate at all, and the systems to be solved in the construction of approximations are 'banded'. The construction of compactly supported smooth piecewise polynomials becomes ever more difficult as the dimension, s, of their domain G ~ IRs, i. e. , the number of arguments, increases. In the univariate case, there is only one kind of cell in any useful partition, namely, an interval, and its boundary consists of two separated points, across which polynomial pieces would have to be matched as one constructs a smooth piecewise polynomial function. This can be done easily, with the only limitation that the num ber of smoothness conditions across such a breakpoint should not exceed the polynomial degree (since that would force the two joining polynomial pieces to coincide). In particular, on any partition, there are (nontrivial) compactly supported piecewise polynomials of degree ~ k and in C(k-l), of which the univariate B-spline is the most useful example.
Download or read book Interpolating Cubic Splines written by Gary D. Knott and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Divided Differences Falling Factorials and Discrete Splines written by Ryan J. Tibshirani and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph reviews a class of univariate piecewise polynomial functions known as discrete splines, which share properties analogous to the better-known class of spline functions, but where continuity in derivatives is replaced by continuity in divided differences. As it happens, discrete splines bear connections to a wide array of developments in applied mathematics and statistics, from divided differences and Newton interpolation, dating back 300 years, to the recent emergence of trend filtering. In this concise yet comprehensive monograph, the author uses his recognized expertise on the subject to guide the reader through these connections. In doing so, the author provides an insightful journey through the historical and most recent developments, contributing some new perspectives and results along the way.Written for researchers and advanced level students of applied mathematics and statistics, this monograph will be of particular interest to those using trend filtering in machine learning applications.
Download or read book Spline and Spline Wavelet Methods with Applications to Signal and Image Processing written by Amir Z. Averbuch and published by Springer Science & Business Media. This book was released on 2014-04-08 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides universal methodologies accompanied by Matlab software to manipulate numerous signal and image processing applications. It is done with discrete and polynomial periodic splines. Various contributions of splines to signal and image processing from a unified perspective are presented. This presentation is based on Zak transform and on Spline Harmonic Analysis (SHA) methodology. SHA combines approximation capabilities of splines with the computational efficiency of the Fast Fourier transform. SHA reduces the design of different spline types such as splines, spline wavelets (SW), wavelet frames (SWF) and wavelet packets (SWP) and their manipulations by simple operations. Digital filters, produced by wavelets design process, give birth to subdivision schemes. Subdivision schemes enable to perform fast explicit computation of splines' values at dyadic and triadic rational points. This is used for signals and images up sampling. In addition to the design of a diverse library of splines, SW, SWP and SWF, this book describes their applications to practical problems. The applications include up sampling, image denoising, recovery from blurred images, hydro-acoustic target detection, to name a few. The SWF are utilized for image restoration that was degraded by noise, blurring and loss of significant number of pixels. The book is accompanied by Matlab based software that demonstrates and implements all the presented algorithms. The book combines extensive theoretical exposure with detailed description of algorithms, applications and software. The Matlab software can be downloaded from http://extras.springer.com
