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Author : Yadvendra Prasad Dubey
Publisher :
ISBN 13 : 9783659279690
Total Pages : 0 pages
Book Rating : 4.2/5 (796 download)
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:
Author : I. J. Schoenberg
Publisher : SIAM
ISBN 13 : 089871009X
Total Pages : 127 pages
Book Rating : 4.8/5 (987 download)
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.
Author : J. H. Ahlberg
Publisher : Elsevier
ISBN 13 : 1483222950
Total Pages : 297 pages
Book Rating : 4.4/5 (832 download)
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.
Author : James B. Cheek
Publisher :
ISBN 13 :
Total Pages : 62 pages
Book Rating : 4.:/5 (359 download)
Download or read book Application of Spline Interpolation Methods to Engineering Problems written by James B. Cheek and published by . This book was released on 1971 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Gary D. Knott
Publisher : Springer Science & Business Media
ISBN 13 : 1461213207
Total Pages : 247 pages
Book Rating : 4.4/5 (612 download)
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.
Author : Borislav D. Bojanov
Publisher : Springer
ISBN 13 : 9780792322290
Total Pages : 292 pages
Book Rating : 4.3/5 (222 download)
Download or read book Spline Functions and Multivariate Interpolations written by Borislav D. Bojanov and published by Springer. This book was released on 1993-03-31 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a comprehensive introduction to the theory of spline functions. Emphasis is given to new developments, such as the general Birkhoff-type interpolation, the extremal properties of splines, their prominent role in the optimal recovery of functions, and multivariate interpolation by polynomials and splines. The book has thirteen chapters dealing, respectively, with interpolation by algebraic polynomials, the space of splines, B-splines, interpolation by spline functions, natural spline functions, perfect splines, monosplines, periodic splines, multivariate B-splines and truncated powers, multivariate spline functions and divided differences, box splines, multivariate mean value interpolation, multivariate polynomial interpolations arising by hyperplanes, and multivariate pointwise interpolation. Some of the results described are presented as exercises and hints are given for their solution. For researchers and graduate students whose work involves approximation theory.
Author : Borislav D. Bojanov
Publisher : Springer Science & Business Media
ISBN 13 : 940158169X
Total Pages : 287 pages
Book Rating : 4.4/5 (15 download)
Download or read book Spline Functions and Multivariate Interpolations written by Borislav D. Bojanov and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Thomas Nall Eden Greville
Publisher :
ISBN 13 :
Total Pages : 31 pages
Book Rating : 4.:/5 (227 download)
Download or read book Another Look at Cubic Spline Interpolation of Equidistant Data written by Thomas Nall Eden Greville and published by . This book was released on 1971 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: A more compact reformulation (probably not generalizable to higher degrees) is given of Schoenberg's explicit construction of interpolating cubic splines with equidistant nodes. (Author).
Author : Stanley G. Rubin
Publisher :
ISBN 13 :
Total Pages : 84 pages
Book Rating : 4.:/5 (31 download)
Download or read book Higher-order Numerical Methods Derived from Three-point Polynomial Interpolation written by Stanley G. Rubin and published by . This book was released on 1976 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Tom Lyche
Publisher :
ISBN 13 : 9788255302117
Total Pages : 40 pages
Book Rating : 4.3/5 (21 download)
Download or read book Discrete Cubic Spline Interpolation written by Tom Lyche and published by . This book was released on 1975 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Yadvendra Dubey
Publisher : LAP Lambert Academic Publishing
ISBN 13 : 9783848403738
Total Pages : 116 pages
Book Rating : 4.4/5 (37 download)
Download or read book Interpolation & Approximation by Spline Function written by Yadvendra Dubey and published by LAP Lambert Academic Publishing. This book was released on 2012-02 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting with the pioneering work of Schoenberg [1], the theory of spline functions and its applications have received much international importance and reorganization in recent years. We very often come across the interpretations of phenomenon in scientific studies which are generally described by functions. Often such functions do not have nice mathematical properties like differentiability, integrability etc. The absence of these useful mathematical properties makes it very difficult to handle with these functions which are so crucial for the study. Thus, in the direction of studies of these functions we replace these functions by an approximating functions having nice mathematical properties. Spline functions are essentially piecewise polynomial functions which meet certain smoothness requirement. The different pieces of spline functions of a certain order provide much greater degree of freedoms in comparison to polynomial functions of the same order. The choice of these degree of freedom in spline functions makes them quite flexible.
Author : Qingkai Kong
Publisher : Academic Press
ISBN 13 : 0128195509
Total Pages : 482 pages
Book Rating : 4.1/5 (281 download)
Download or read book Python Programming and Numerical Methods written by Qingkai Kong and published by Academic Press. This book was released on 2020-11-27 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: Python Programming and Numerical Methods: A Guide for Engineers and Scientists introduces programming tools and numerical methods to engineering and science students, with the goal of helping the students to develop good computational problem-solving techniques through the use of numerical methods and the Python programming language. Part One introduces fundamental programming concepts, using simple examples to put new concepts quickly into practice. Part Two covers the fundamentals of algorithms and numerical analysis at a level that allows students to quickly apply results in practical settings. Includes tips, warnings and "try this" features within each chapter to help the reader develop good programming practice Summaries at the end of each chapter allow for quick access to important information Includes code in Jupyter notebook format that can be directly run online
Author : C. K. Chui
Publisher :
ISBN 13 :
Total Pages : 45 pages
Book Rating : 4.:/5 (16 download)
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.
Author : T. N. E. Greville
Publisher :
ISBN 13 :
Total Pages : 49 pages
Book Rating : 4.:/5 (247 download)
Download or read book Interpolation by Generalized Spline Functions written by T. N. E. Greville and published by . This book was released on 1964 with total page 49 pages. Available in PDF, EPUB and Kindle. Book excerpt: A spline function is a function defined by piecewise polynomial arcs joined so that derivatives are continuous everywhere up to and including the order one less than the degree of polynomials used. Various aspects of interpolation by spline functions have been considered by a number of writers. The problem under consideration is that of inter polating for a function of one variable between a number of data points (not necessarily equally spaced) obtained with sufficient accuracy so that errors of measurement can be considered negligible in comparison with the error involved in interpolation. If the physical system or process which gave rise to the measurements is highly complex, it may be impractical to determine explicitly or to calculate values of the underlying function. The advantages of spline-function interpolation in such situations have been previously pointed out. Continuity of low-order derivatives is secured while largely or wholly avoiding the spurious undulations that commonly result from the use of a polynomial of sufficiently high degree to fit all data points exactly.
Author : Yadvendra Prasad Dubey
Publisher :
ISBN 13 : 9783659260834
Total Pages : 0 pages
Book Rating : 4.2/5 (68 download)
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:
Author : Helmuth Späth
Publisher : CRC Press
ISBN 13 : 1439864721
Total Pages : 312 pages
Book Rating : 4.4/5 (398 download)
Download or read book Two Dimensional Spline Interpolation Algorithms written by Helmuth Späth and published by CRC Press. This book was released on 1993-05-31 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: These volumes present a practical introduction to computing spline functions, the fundamental tools for fitting curves and surfaces in computer-aided deisgn (CAD) and computer graphics.
Author : Richard H. Bartels
Publisher : Morgan Kaufmann
ISBN 13 : 9781558604001
Total Pages : 504 pages
Book Rating : 4.6/5 (4 download)
Download or read book An Introduction to Splines for Use in Computer Graphics and Geometric Modeling written by Richard H. Bartels and published by Morgan Kaufmann. This book was released on 1995-09 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: As the field of computer graphics develops, techniques for modeling complex curves and surfaces are increasingly important. A major technique is the use of parametric splines in which a curve is defined by piecing together a succession of curve segments, and surfaces are defined by stitching together a mosaic of surface patches. An Introduction to Splines for Use in Computer Graphics and Geometric Modeling discusses the use of splines from the point of view of the computer scientist. Assuming only a background in beginning calculus, the authors present the material using many examples and illustrations with the goal of building the reader's intuition. Based on courses given at the University of California, Berkeley, and the University of Waterloo, as well as numerous ACM Siggraph tutorials, the book includes the most recent advances in computer-aided geometric modeling and design to make spline modeling techniques generally accessible to the computer graphics and geometric modeling communities.
