On Interpolation And Best One Sided Approximation By Splines In Lp PDF Download
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| Author | : Günther Nürnberger |
| Publisher | : Springer |
| Total Pages | : 244 |
| Release | : 2013-11-20 |
| Genre | : Mathematics |
| ISBN | : 9783642647994 |
Download Approximation by Spline Functions Book in PDF, ePub and Kindle
Splines play an important role in applied mathematics since they possess high flexibility to approximate efficiently, even nonsmooth functions which are given explicitly or only implicitly, e.g. by differential equations. The aim of this book is to analyse in a unified approach basic theoretical and numerical aspects of interpolation and best approximation by splines in one variable. The first part on spaces of polynomials serves as a basis for investigating the more complex structure of spline spaces. Given in the appendix are brief introductions to the theory of splines with free knots (an algorithm is described in the main part), to splines in two variables and to spline collocation for differential equations.A large number of new results presented here cannot be found in earlier books on splines. Researchers will find several references to recent developments. The book is an indispensable aid for graduate courses on splines or approximation theory. Students with a basic knowledge of analysis and linear algebra will be able to read the text. Engineers will find various pactical interpolation and approximation methods.
| Author | : J. Prestin |
| Publisher | : |
| Total Pages | : 12 |
| Release | : 1991 |
| Genre | : Approximation theory |
| ISBN | : |
Download On Interpolation and Best One-sided Approximation by Splines in L^p Book in PDF, ePub and Kindle
The aim of this paper is to give quantitative L^p-error estimates for periodic spline interpolants in terms of the best one-sided spline approximation. In this context Marcinkiewicz-Zygmund type inequalities play an important role. In particular, cubic C1-interpolation is considered.
| Author | : Boris I Kvasov |
| Publisher | : World Scientific |
| Total Pages | : 356 |
| Release | : 2000-07-24 |
| Genre | : Mathematics |
| ISBN | : 981449447X |
Download Methods Of Shape-preserving Spline Approximation Book in PDF, ePub and Kindle
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 | : Samuel Karlin |
| Publisher | : |
| Total Pages | : 520 |
| Release | : 1976 |
| Genre | : Mathematics |
| ISBN | : |
Download Studies in Spline Functions and Approximation Theory Book in PDF, ePub and Kindle
This volume reports a series of research investigations concerned with spline functions and approximation theory. The common thread of the studies derives from the facts that (1) the subject matter of the individual articles relate and significantly complement each other; 92) part of the genesis and certainly the main developments of these studies occurred at the Weizmann Institute of Science, Rehovot, Israel, commencing about September 1970 through June 1974. The contributions cover aspects of the theory of best approximation and quadratures, the solution of certain extremal problems embracing generalized Landau and Markov-type inequalities for derivative functionals, and a hierarchy of interpolation and convergence properties of classes of spline functions.
| Author | : I. J. Schoenberg |
| Publisher | : SIAM |
| Total Pages | : 131 |
| Release | : 1973-01-01 |
| Genre | : Mathematics |
| ISBN | : 9781611970555 |
Download Cardinal Spline Interpolation Book in PDF, ePub and Kindle
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 | : P. M. Prenter |
| Publisher | : Wiley-Interscience |
| Total Pages | : 342 |
| Release | : 1975 |
| Genre | : Mathematics |
| ISBN | : |
Download Splines and Variational Methods Book in PDF, ePub and Kindle
Introduction ideas; Lagrangian interpolates; Hermitian interpolates; Polynomial splines and generalizations; Approximating functions of several variables; Fundamentals for variational methods; The finite element method; The method of collocation; Index.
| Author | : Charles B. (Charles Burton) Dunham |
| Publisher | : London : Department of Computer Science, University of Western Ontario |
| Total Pages | : 5 |
| Release | : 1988 |
| Genre | : |
| ISBN | : 9780771410215 |
Download An Interpolation Theorem for Discrete One-sided Non-linear Lp (p[greater Than Or Equal To] 1) Approximation Book in PDF, ePub and Kindle
| Author | : Peter Robert Massopust |
| Publisher | : |
| Total Pages | : 344 |
| Release | : 2010 |
| Genre | : Computers |
| ISBN | : |
Download Interpolation and Approximation with Splines and Fractals Book in PDF, ePub and Kindle
This textbook is intended to supplement the classical theory of uni- and multivariate splines and their approximation and interpolation properties with those of fractals, fractal functions, and fractal surfaces. This synthesis will complement currently required courses dealing with these topics and expose the prospective reader to some new and deep relationships. In addition to providing a classical introduction to the main issues involving approximation and interpolation with uni- and multivariate splines, cardinal and exponential splines, and their connection to wavelets and multiscale analysis, which comprises the first half of the book, the second half will describe fractals, fractal functions and fractal surfaces, and their properties. This also includes the new burgeoning theory of superfractals and superfractal functions. The theory of splines is well-established but the relationship to fractal functions is novel. Throughout the book, connections between these two apparently different areas will be exposed and presented. In this way, more options are given to the prospective reader who will encounter complex approximation and interpolation problems in real-world modeling. Numerous examples, figures, and exercises accompany the material.
| Author | : George Anastassiou |
| Publisher | : CRC Press |
| Total Pages | : 558 |
| Release | : 1992-04-24 |
| Genre | : Mathematics |
| ISBN | : 9780824787080 |
Download Approximation Theory Book in PDF, ePub and Kindle
Contains the proceedings of the March 1991 annual conference of the Southeastern Approximation Theorists, in Memphis, Tenn. The 34 papers discuss topics of interest to graduate and professional numerical analysts, applied and industrial mathematicians, engineers, and other scientists such as splines
| Author | : Borislav D. Bojanov |
| Publisher | : Springer |
| Total Pages | : 292 |
| Release | : 1993-03-31 |
| Genre | : Computers |
| ISBN | : 9780792322290 |
Download Spline Functions and Multivariate Interpolations Book in PDF, ePub and Kindle
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.
