Some Problems In Cardinal Spline Interpolation And Approximation

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Cardinal Spline Interpolation

Author : I. J. Schoenberg
Publisher : SIAM
ISBN 13 : 9781611970555
Total Pages : 131 pages
Book Rating : 4.9/5 (75 download)

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Book Synopsis Cardinal Spline Interpolation by : I. J. Schoenberg

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 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Some Problems in Cardinal Spline Interpolation and Approximation

Author : Daniel Tien-You Lee
Publisher :
ISBN 13 :
Total Pages : 142 pages
Book Rating : 4.:/5 (89 download)

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Book Synopsis Some Problems in Cardinal Spline Interpolation and Approximation by : Daniel Tien-You Lee

Download or read book Some Problems in Cardinal Spline Interpolation and Approximation written by Daniel Tien-You Lee and published by . This book was released on 1984 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Studies in Spline Functions and Approximation Theory

Author : Samuel Karlin
Publisher :
ISBN 13 :
Total Pages : 520 pages
Book Rating : 4.:/5 (5 download)

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Book Synopsis Studies in Spline Functions and Approximation Theory by : Samuel Karlin

Download or read book Studies in Spline Functions and Approximation Theory written by Samuel Karlin and published by . This book was released on 1976 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Methods of Shape-preserving Spline Approximation

Author : Boris I. Kvasov
Publisher : World Scientific
ISBN 13 : 9789810240103
Total Pages : 360 pages
Book Rating : 4.2/5 (41 download)

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Book Synopsis Methods of Shape-preserving Spline Approximation by : Boris I. Kvasov

Download or read book Methods of Shape-preserving Spline Approximation written by Boris I. Kvasov and published by World Scientific. This book was released on 2000 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Interpolation and Approximation with Splines and Fractals

Author : Peter Robert Massopust
Publisher :
ISBN 13 :
Total Pages : 344 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Interpolation and Approximation with Splines and Fractals by : Peter Robert Massopust

Download or read book Interpolation and Approximation with Splines and Fractals written by Peter Robert Massopust and published by . This book was released on 2010 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Polynomial and Spline Approximation

Author : B.N. Sahney
Publisher : Springer
ISBN 13 :
Total Pages : 344 pages
Book Rating : 4.:/5 (5 download)

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Book Synopsis Polynomial and Spline Approximation by : B.N. Sahney

Download or read book Polynomial and Spline Approximation written by B.N. Sahney and published by Springer. This book was released on 1979-05-31 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Study Institute, Calgary, Canada, August 26-September 2, 1978

Approximation Theory and Applications

Author : Zvi Ziegler
Publisher :
ISBN 13 :
Total Pages : 384 pages
Book Rating : 4.:/5 (49 download)

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Book Synopsis Approximation Theory and Applications by : Zvi Ziegler

Download or read book Approximation Theory and Applications written by Zvi Ziegler and published by . This book was released on 1981 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Construction of elements of the relative chebyshev center. The numerical claculation of spline approximations on a binfinite. Global analysis in nonlinear approximation and its application to exponential approximation. Global analysis in nonlinear approximation and its application to exponential approximation. Simultaneous approximation and restricted chebyshev centers in function spaces. Quelques proprietes D'Une family D'operateurs positfs sur des espaces de functions relles definies presque partout sur ... Bell-Shaped basis functions for surface fitting. The n-Widhts of sets of analytic functions. Admissibility of quadrature formulas with random nodes. Convergence for operators of hyperbolic type. Explicit ... - extensions of functions of two variebles in a strip between two curves, or in a corner in IR ... Taylor interpolation of order n at the vertices of a triangle. Applications for hermite interpolation and finite elements. Jacobi projections. Oscillating monosplines of least uniform norm. Some applications and drawbacks of padé approximants. From dirac distributions to multivariate representation formulas. A new iterative method for the solution of systems nonlinear equations. Polynomials and rational functions. Quadrature formulae based on shape preserving interpolation. Optimal recovery among the polynomials. On cardinal spline interpolants. Approximation by lacunary polynomials: A converse theorem. An interpolatory rational approximation. Design problems for optimal surface interpolation. Open problems.

Topics in Multivariate Approximation

Author : C. K. Chui
Publisher : Elsevier
ISBN 13 : 1483271005
Total Pages : 346 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Topics in Multivariate Approximation by : C. K. Chui

Download or read book Topics in Multivariate Approximation written by C. K. Chui and published by Elsevier. This book was released on 2014-05-10 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Spline Interpolation and Some Related Topics

Author : Rong-Qing Jia
Publisher :
ISBN 13 :
Total Pages : 186 pages
Book Rating : 4.:/5 (89 download)

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Book Synopsis Spline Interpolation and Some Related Topics by : Rong-Qing Jia

Download or read book Spline Interpolation and Some Related Topics written by Rong-Qing Jia and published by . This book was released on 1983 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Approximation Theory, Spline Functions and Applications

Author : S.P. Singh
Publisher : Springer Science & Business Media
ISBN 13 : 9401126348
Total Pages : 482 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Approximation Theory, Spline Functions and Applications by : S.P. Singh

Download or read book Approximation Theory, Spline Functions and Applications written by S.P. Singh and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: These are the Proceedings of the NATO Advanced Study Institute on Approximation Theory, Spline Functions and Applications held in the Hotel villa del Mare, Maratea, Italy between April 28,1991 and May 9, 1991. The principal aim of the Advanced Study Institute, as reflected in these Proceedings, was to bring together recent and up-to-date developments of the subject, and to give directions for future research. Amongst the main topics covered during this Advanced Study Institute is the subject of uni variate and multivariate wavelet decomposition over spline spaces. This is a relatively new area in approximation theory and an increasingly impor tant subject. The work involves key techniques in approximation theory cardinal splines, B-splines, Euler-Frobenius polynomials, spline spaces with non-uniform knot sequences. A number of scientific applications are also highlighted, most notably applications to signal processing and digital im age processing. Developments in the area of approximation of functions examined in the course of our discussions include approximation of periodic phenomena over irregular node distributions, scattered data interpolation, Pade approximants in one and several variables, approximation properties of weighted Chebyshev polynomials, minimax approximations, and the Strang Fix conditions and their relation to radial functions. I express my sincere thanks to the members of the Advisory Commit tee, Professors B. Beauzamy, E. W. Cheney, J. Meinguet, D. Roux, and G. M. Phillips. My sincere appreciation and thanks go to A. Carbone, E. DePas cale, R. Charron, and B.

Cardinal Spline Interpolation

Author : I. J. Schoenberg
Publisher : SIAM
ISBN 13 : 089871009X
Total Pages : 127 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Cardinal Spline Interpolation by : I. J. Schoenberg

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.

Bivariate Cardinal Interpolation by Splines on a Three-Direction Mesh

Author : Carl de Boor
Publisher :
ISBN 13 :
Total Pages : 40 pages
Book Rating : 4.:/5 (227 download)

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Book Synopsis Bivariate Cardinal Interpolation by Splines on a Three-Direction Mesh by : Carl de Boor

Download or read book Bivariate Cardinal Interpolation by Splines on a Three-Direction Mesh written by Carl de Boor and published by . This book was released on 1983 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a series of monographs Schogenberg developed a comprehensive theory of univariate cardinal splines. His results strongly influenced the analysis of totally positive matrices. In this report the author extend two of his basic results on cardinal interpolation to bivariate box-splines. They show that, for functions of exponential type, cardinal interpolation is a rapidly convergent approximation process as the degree tends to infinity. Being not restricted to a tensor product mesh gives a greater flexibility, and because of the exponential decay of the Lagrange functions, spline interpolation is suitable, e.g., for data smoothing. They also expect that bivariate cardinal splines have a similar significance for theoretical questions as in the univariate case.

Approximation in Theorie und Praxis

Author : Günther Meinardus
Publisher :
ISBN 13 :
Total Pages : 318 pages
Book Rating : 4.:/5 (5 download)

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Book Synopsis Approximation in Theorie und Praxis by : Günther Meinardus

Download or read book Approximation in Theorie und Praxis written by Günther Meinardus and published by . This book was released on 1979 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Handbook of Splines

Author : Gheorghe Micula
Publisher : Springer Science & Business Media
ISBN 13 : 9401153388
Total Pages : 622 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Handbook of Splines by : Gheorghe Micula

Download or read book Handbook of Splines written by Gheorghe Micula and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Spline Functions and Multivariate Interpolations

Author : Borislav D. Bojanov
Publisher : Springer
ISBN 13 : 9789401581707
Total Pages : 278 pages
Book Rating : 4.5/5 (817 download)

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Book Synopsis Spline Functions and Multivariate Interpolations by : Borislav D. Bojanov

Download or read book Spline Functions and Multivariate Interpolations written by Borislav D. Bojanov and published by Springer. This book was released on 2014-03-14 with total page 278 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.

Off-Knot Spline Interpolation and Constrained Approximation: Some Negative Results

Author : James W. Daniel
Publisher :
ISBN 13 :
Total Pages : 22 pages
Book Rating : 4.:/5 (227 download)

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Book Synopsis Off-Knot Spline Interpolation and Constrained Approximation: Some Negative Results by : James W. Daniel

Download or read book Off-Knot Spline Interpolation and Constrained Approximation: Some Negative Results written by James W. Daniel and published by . This book was released on 1974 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quadratic splines are generated which interpolate a function and its derivative at points midway between alternate pairs of knots, and the error bound is shown to be precisely of order (h sup 2) rather than (h sup 3) as expected. This result is related to best constrained approximation by splines and thence to Galerkin methods for constrained problems. (Author).

Interpolating Cubic Splines

Author : Gary D. Knott
Publisher : Springer Science & Business Media
ISBN 13 : 9780817641009
Total Pages : 316 pages
Book Rating : 4.6/5 (41 download)

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Book Synopsis Interpolating Cubic Splines by : Gary D. Knott

Download or read book Interpolating Cubic Splines written by Gary D. Knott and published by Springer Science & Business Media. This book was released on 1999 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of spline functions is an outgrowth of basic mathematical concepts arising from calculus, analysis and numerical analysis. Spline modelling affects a number of fields: statistics; computer graphics; CAD programming, and other areas of applied mathematics.