[PDF] Discrete Polynomial Splines eBook

Author : Boris I. Kvasov
Publisher : World Scientific
Page : 360 pages
File Size : 12,80 MB
Release : 2000
Category : Mathematics
ISBN : 9789810240103

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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.

Author : Amir Z. Averbuch
Publisher : Springer
Page : 441 pages
File Size : 39,12 MB
Release : 2015-08-27
Category : Technology & Engineering
ISBN : 3319223038

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This book presents various contributions of splines to signal and image processing from a unified perspective that is based on the Zak transform (ZT). It expands the methodology from periodic splines, which were presented in the first volume, to non-periodic splines. Together, these books provide a universal toolbox accompanied by MATLAB software for manipulating polynomial and discrete splines, spline-based wavelets, wavelet packets and wavelet frames for signal/ image processing applications. In this volume, we see that the ZT provides an integral representation of discrete and polynomial splines, which, to some extent, is similar to Fourier integral. The authors explore elements of spline theory and design, and consider different types of polynomial and discrete splines. They describe applications of spline-based wavelets to data compression. These splines are useful for real-time signal processing and, in particular, real-time wavelet and frame transforms. Further topics addressed in this volume include: "global" splines, such as interpolating, self-dual and smoothing, whose supports are infinite; the compactly supported quasi-interpolating and smoothing splines including quasi-interpolating splines on non-uniform grids; and cubic Hermite splines as a source for the design of multiwavelets and multiwavelet frames. Readers from various disciplines including engineering, computer science and mathematical information technology will find the descriptions of algorithms, applications and software in this book especially useful.

Author : J. H. Ahlberg
Publisher : Elsevier
Page : 297 pages
File Size : 43,69 MB
Release : 2016-06-03
Category : Mathematics
ISBN : 1483222950

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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 : B.N. Sahney
Publisher : Springer
Page : 344 pages
File Size : 30,86 MB
Release : 1979-05-31
Category : Mathematics
ISBN :

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Proceedings of the NATO Advanced Study Institute, Calgary, Canada, August 26-September 2, 1978

Author : Ryan J. Tibshirani
Publisher :
Page : 0 pages
File Size : 16,11 MB
Release : 2022-07-21
Category : Machine learning
ISBN : 9781638280361

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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.