Smoothing and Multivariate Interpolation with Splines PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Smoothing and Multivariate Interpolation with Splines PDF full book. Access full book title Smoothing and Multivariate Interpolation with Splines by T. L. Jordan. Download full books in PDF and EPUB format.
Author: T. L. Jordan
Publisher:
ISBN:
Category : Numerical analysis
Languages : en
Pages : 26
Get Book Here
Book Description
Author: T. L. Jordan
Publisher:
ISBN:
Category : Numerical analysis
Languages : en
Pages : 26
Get Book Here
Book Description
Author: Borislav D. Bojanov
Publisher: Springer Science & Business Media
ISBN: 940158169X
Category : Mathematics
Languages : en
Pages : 287
Get Book Here
Book Description
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: Charles K. Chui
Publisher: SIAM
ISBN: 0898712262
Category : Mathematics
Languages : en
Pages : 192
Get Book Here
Book Description
Subject of multivariate splines presented from an elementary point of view; includes many open problems.
Author: C. K. Chui
Publisher: Elsevier
ISBN: 1483271005
Category : Mathematics
Languages : en
Pages : 346
Get Book Here
Book Description
Topics in Multivariate Approximation contains the proceedings of an international workshop on multivariate approximation held at the University of Chile in Santiago, Chile, on December 15-19, 1986. Leading researchers in the field discussed several problem areas related to multivariate approximation and tackled topics ranging from multivariate splines and fitting of scattered data to tensor approximation methods and multivariate polynomial approximation. Numerical grid generation and finite element methods were also explored, along with constrained interpolation and smoothing. Comprised of 22 chapters, this book first describes the application of Boolean methods of approximation in combination with the theory of right invertible operators to bivariate Fourier expansions. The reader is then introduced to ill-posed problems in multivariate approximation; interpolation of scattered data by radial functions; and shape-preserving surface interpolation. Subsequent chapters focus on approximation by harmonic functions; numerical generation of nested series of general triangular grids; triangulation methods; and inequalities arising from best local approximations in rectangles. A bibliography of multivariate approximation concludes the book. This monograph will be of interest to mathematicians.
Author: Borislav D. Bojanov
Publisher: Springer
ISBN: 9780792322290
Category : Computers
Languages : en
Pages : 292
Get Book Here
Book Description
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: Anatoly Yu. Bezhaev
Publisher: Springer Science & Business Media
ISBN: 147573428X
Category : Mathematics
Languages : en
Pages : 291
Get Book Here
Book Description
This book is a systematic description of the variational theory of splines in Hilbert spaces. All central aspects are discussed in the general form: existence, uniqueness, characterization via reproducing mappings and kernels, convergence, error estimations, vector and tensor hybrids in splines, dimensional reducing (traces of splines onto manifolds), etc. All considerations are illustrated by practical examples. In every case the numerical algorithms for the construction of splines are demonstrated.
Author: J. Braselton
Publisher: CreateSpace
ISBN: 9781502332462
Category : Mathematics
Languages : en
Pages : 114
Get Book Here
Book Description
Curve Fitting Toolbox provides graphical tools and command-line functions for fitting curves and surfaces to data. The toolbox lets you perform exploratory data analysis, preprocess and post-process data, compare candidate models, and remove outliers. You can conduct regression analysis using the library of linear and nonlinear models provided or specify your own custom equations. The library provides optimized solver parameters and starting conditions to improve the quality of your fits. The toolbox also supports nonparametric modeling techniques, such as splines, interpolation, and smoothing. After creating a fit, you can apply a variety of post-processing methods for plotting, interpolation, and extrapolation; estimating confidence intervals; and calculating integrals and derivatives. The most important topics in this book are: Interactive Spline Fitting Programmatic Spline Fitting Curve Fitting Toolbox Splines MATLAB Splines Expected Background Vector Data Type Support Spline Function Naming Conventions Arguments for Curve Fitting Toolbox Spline Functions Cubic Spline Interpolation Cubic Spline Interpolant of Smooth Data Periodic Data Other End Conditions General Spline Interpolation Knot Choices Smoothing Least Squares Vector-Valued Functions Fitting Values at N-D Grid with Tensor-Product Splines Fitting Values at Scattered 2-D Sites with Thin-Plate Smoothing Splines Postprocessing Splines B-Splines and Smoothing Splines Multivariate and Rational SplinesLeast-Squares Approximation by Natural Cubic Splines Solving A Nonlinear ODE Construction of the Chebyshev Spline Approximation by Tensor Product Splines
Author: Paul H.C. Eilers
Publisher: Cambridge University Press
ISBN: 1108686885
Category : Computers
Languages : en
Pages : 213
Get Book Here
Book Description
This is a practical guide to P-splines, a simple, flexible and powerful tool for smoothing. P-splines combine regression on B-splines with simple, discrete, roughness penalties. They were introduced by the authors in 1996 and have been used in many diverse applications. The regression basis makes it straightforward to handle non-normal data, like in generalized linear models. The authors demonstrate optimal smoothing, using mixed model technology and Bayesian estimation, in addition to classical tools like cross-validation and AIC, covering theory and applications with code in R. Going far beyond simple smoothing, they also show how to use P-splines for regression on signals, varying-coefficient models, quantile and expectile smoothing, and composite links for grouped data. Penalties are the crucial elements of P-splines; with proper modifications they can handle periodic and circular data as well as shape constraints. Combining penalties with tensor products of B-splines extends these attractive properties to multiple dimensions. An appendix offers a systematic comparison to other smoothers.
Author: Yuedong Wang
Publisher: CRC Press
ISBN: 1420077562
Category : Computers
Languages : en
Pages : 380
Get Book Here
Book Description
A general class of powerful and flexible modeling techniques, spline smoothing has attracted a great deal of research attention in recent years and has been widely used in many application areas, from medicine to economics. Smoothing Splines: Methods and Applications covers basic smoothing spline models, including polynomial, periodic, spherical, t
Author: Gheorghe Micula
Publisher: Springer Science & Business Media
ISBN: 9401153388
Category : Mathematics
Languages : en
Pages : 622
Get Book Here
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.
