Author: James B. Cheek Publisher: ISBN: Category : Curve fitting Languages : en Pages : 62
Book Description
This paper was prepared to familiarize practicing scientists and engineers with the cubic spline interpolation technique as a possible tool in curve fitting for computer programs for which more commonly used techniques may be unsuitable or of limited value. The spline technique is compared with more common methods, specifically piecewise linear and polynomial, and examples of applications of the technique to engineering problems are presented.
Author: P. M. Prenter Publisher: Courier Corporation ISBN: 0486783499 Category : Mathematics Languages : en Pages : 338
Book Description
One of the clearest available introductions to variational methods, this text requires only a minimal background in calculus and linear algebra. Its self-contained treatment explains the application of theoretic notions to the kinds of physical problems that engineers regularly encounter. The text’s first half concerns approximation theoretic notions, exploring the theory and computation of one- and two-dimensional polynomial and other spline functions. Later chapters examine variational methods in the solution of operator equations, focusing on boundary value problems in one and two dimensions. Additional topics include least squares and other Galerkin methods. Many helpful definitions, examples, and exercises appear throughout the book. A classic reference in spline theory, this volume will benefit experts as well as students of engineering and mathematics.
Author: I. J. Schoenberg Publisher: SIAM ISBN: 9781611970555 Category : Mathematics Languages : en Pages : 131
Book Description
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: Elena A. Shirokova Publisher: Bentham Science Publishers ISBN: 1608052095 Category : Science Languages : en Pages : 268
Book Description
"The book presents methods of approximate solution of the basic problem of elasticity for special types of solids. Engineers can apply the approximate methods (Finite Element Method, Boundary Element Method) to solve the problems but the application of the"
Author: Charles K. Chui Publisher: ISBN: Category : Languages : en Pages : 24
Book Description
The notion of super splines and vertex splines is introduced and studied. Quasi-interpolation formulas for real-time applications are constructed. The method of noncommutative blending of quasi-interpolation and vertex spline interpolation is introduced to yield interpolation schemes which are local, flexible, and of optimal approximation orders. These formulas can be applied to real-time interpolation by means of table-look-up or FIR implementation. Applications to engineering problems such as parallel implementation of the extended Kalman filter and Hankel-norm frequency domain methods are studied. Wavelets are constructed by applying cardinal splines, and hence, they are readily available for real-time interpolation and orthogonal wavelet decompositions and reconstructions. (KR).
Author: Paul Dierckx Publisher: Oxford University Press ISBN: 9780198534402 Category : Computers Languages : en Pages : 308
Book Description
The fitting of a curve or surface through a set of observational data is a very frequent problem in different disciplines (mathematics, engineering, medicine, ...) with many interesting applications. This book describes the algorithms and mathematical fundamentals of a widely used software package for data fitting with (tensor product) splines. As such it gives a survey of possibilities and benefits but also of the problems to cope with when approximating with this popular type of function. In particular it is demonstrated in detail how the properties of B-splines can be fully exploited for improving the computational efficiency and for incorporating different boundary or shape preserving constraints. Special attention is also paid to strategies for an automatic and adaptive knot selection with intent to obtain serious data reductions. The practical use of the smoothing software is illustrated with many examples, academic as well as taken from real life.
Author: Boris I. Kvasov Publisher: World Scientific ISBN: 9789810240103 Category : Mathematics Languages : en Pages : 360
Book Description
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: Young Kinh-Nhue Truong Publisher: BoD – Books on Demand ISBN: 1789232503 Category : Computers Languages : en Pages : 162
Book Description
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: Gheorghe Micula Publisher: Springer Science & Business Media ISBN: 9401153388 Category : Mathematics Languages : en Pages : 622
Book Description
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: James B. Cheek
Author: P. M. Prenter
Author: I. J. Schoenberg
Author: Elena A. Shirokova
Author: Charles K. Chui
Author: Paul Dierckx
Author: Homer Bruce Sallee
Author: Boris I. Kvasov
Author: Young Kinh-Nhue Truong
Author: Gheorghe Micula