Download or read book On Lagrange Polynomial Quasi interpolation written by C. K. Chui and published by . This book was released on 1990 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: For H^{\infty} functions whose radial limits are almost everywhere continuous on the unit circle in the complex plane, we give an estimate, in terms of the average modulus of continuity, for approximation using Lagrange interpolating, and more generally quasi-interpolating, polynomials at the nth roots of unity. Our error estimate not only improves the existing results on Lagrange interpolation using the uniform modulus of continuity, but also gives an estimation for the Motzkin-Sharma quasi-interpolatory polynomial approximation. Furthermore, our results can be easily modified to give error estimations for more general interpolatory processes such as the Hermite-Fejér interpolation.
Download or read book Lagrange Interpolation and Quasi interpolation Using Trivariate Splines on a Uniform Partition written by Georg Hubert Schneider and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quasi Interpolation written by Martin Buhmann and published by Cambridge University Press. This book was released on 2022-03-03 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Quasi-interpolation is one of the most useful and often applied methods for the approximation of functions and data in mathematics and applications. Its advantages are manifold: quasi-interpolants are able to approximate in any number of dimensions, they are efficient and relatively easy to formulate for scattered and meshed nodes and for any number of data. This book provides an introduction into the field for graduate students and researchers, outlining all the mathematical background and methods of implementation. The mathematical analysis of quasi-interpolation is given in three directions, namely on the basis (spline spaces, radial basis functions) from which the approximation is taken, on the form and computation of the quasi-interpolants (point evaluations, averages, least squares), and on the mathematical properties (existence, locality, convergence questions, precision). Learn which type of quasi-interpolation to use in different contexts and how to optimise its features to suit applications in physics and engineering.
Download or read book Interpolation of Functions written by J. Szabados and published by World Scientific. This book was released on 1990 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a systematic survey on the most significant results of interpolation theory in the last forty years. It deals with Lagrange interpolation including lower estimates, fine and rough theory, interpolatory proofs of Jackson and Teliakovski-Gopengauz theorems, Lebesgue function, Lebesgue constant of Lagrange interpolation, Bernstein and Erdös conjecture on the optimal nodes, the almost everywhere divergence of Lagrange interpolation for arbitrary system of nodes, Hermite-Fejer type and lacunary interpolation and other related topics.
Download or read book Frontiers in Interpolation and Approximation written by N. K. Govil and published by CRC Press. This book was released on 2006-07-20 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dedicated to the well-respected research mathematician Ambikeshwar Sharma, Frontiers in Interpolation and Approximation explores approximation theory, interpolation theory, and classical analysis. Written by authoritative international mathematicians, this book presents many important results in classical analysis, wavelets, and interpolation theory. Some topics covered are Markov inequalities for multivariate polynomials, analogues of Chebyshev and Bernstein inequalities for multivariate polynomials, various measures of the smoothness of functions, and the equivalence of Hausdorff continuity and pointwise Hausdorff-Lipschitz continuity of a restricted center multifunction. The book also provides basic facts about interpolation, discussing classes of entire functions such as algebraic polynomials, trigonometric polynomials, and nonperiodic transcendental entire functions. Containing both original research and comprehensive surveys, this book provides researchers and graduate students with important results of interpolation and approximation.
Download or read book Estimation of Complex Quasi interpolatory Approximation Using Average Modulus of Continuity written by C. K. Chui and published by . This book was released on 1990 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: For H^{\infty} functions whose radial limits are almost everywhere continuous on the unit circle in the complex plane, we give an estimate, in terms of the average modulus of continuity, for approximation using Lagrange interpolating, and more generally quasi-interpolating, polynomials at the nth roots of unity. Our error estimate not only improves the existing results on Lagrange interpolation using the uniform modulus of continuity, but also gives an estimation for the Motzkin-Sharma quasi-interpolatory polynomial approximation. Furthermore, our results can be easily modified to give error estimations for more general interpolatory processes such as the Hermite-Fejér interpolation.
Download or read book Interpolation and Extrapolation Optimal Designs V1 written by Giorgio Celant and published by John Wiley & Sons. This book was released on 2016-06-07 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first of a series which focuses on the interpolation and extrapolation of optimal designs, an area with significant applications in engineering, physics, chemistry and most experimental fields. In this volume, the authors emphasize the importance of problems associated with the construction of design. After a brief introduction on how the theory of optimal designs meets the theory of the uniform approximation of functions, the authors introduce the basic elements to design planning and link the statistical theory of optimal design and the theory of the uniform approximation of functions. The appendices provide the reader with material to accompany the proofs discussed throughout the book.
Download or read book Topics in Polynomials of One and Several Variables and Their Applications written by Themistocles M. Rassias and published by World Scientific. This book was released on 1993 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents an account of some of the most important work that has been done on various research problems in the theory of polynomials of one and several variables and their applications. It is dedicated to P L Chebyshev, a leading Russian mathematician.
Download or read book General Lagrangian Interpolation Formulas written by C. E. Velez and published by . This book was released on 1968 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Approximation Theory Wavelets and Applications written by S.P. Singh and published by Springer. This book was released on 1995-01-31 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approximation Theory, Wavelets and Applications draws together the latest developments in the subject, provides directions for future research, and paves the way for collaborative research. The main topics covered include constructive multivariate approximation, theory of splines, spline wavelets, polynomial and trigonometric wavelets, interpolation theory, polynomial and rational approximation. Among the scientific applications were de-noising using wavelets, including the de-noising of speech and images, and signal and digital image processing. In the area of the approximation of functions the main topics include multivariate interpolation, quasi-interpolation, polynomial approximation with weights, knot removal for scattered data, convergence theorems in Padé theory, Lyapunov theory in approximation, Neville elimination as applied to shape preserving presentation of curves, interpolating positive linear operators, interpolation from a convex subset of Hilbert space, and interpolation on the triangle and simplex. Wavelet theory is growing extremely rapidly and has applications which will interest readers in the physical, medical, engineering and social sciences.
Download or read book Approximation Theory Wavelets and Applications written by S.P. Singh and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approximation Theory, Wavelets and Applications draws together the latest developments in the subject, provides directions for future research, and paves the way for collaborative research. The main topics covered include constructive multivariate approximation, theory of splines, spline wavelets, polynomial and trigonometric wavelets, interpolation theory, polynomial and rational approximation. Among the scientific applications were de-noising using wavelets, including the de-noising of speech and images, and signal and digital image processing. In the area of the approximation of functions the main topics include multivariate interpolation, quasi-interpolation, polynomial approximation with weights, knot removal for scattered data, convergence theorems in Padé theory, Lyapunov theory in approximation, Neville elimination as applied to shape preserving presentation of curves, interpolating positive linear operators, interpolation from a convex subset of Hilbert space, and interpolation on the triangle and simplex. Wavelet theory is growing extremely rapidly and has applications which will interest readers in the physical, medical, engineering and social sciences.
Download or read book Computation of Curves and Surfaces written by Wolfgang Dahmen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assembled here is a collection of articles presented at a NATO ADVANCED STU DY INSTITUTE held at Puerto de la Cruz, Tenerife, Spain during the period of July 10th to 21st, 1989. In addition to the editors of these proceedings Professor Larry L. Schumaker from Vanderbilt University, Nashville, Tennessee, served as a member of the international organizing committee. The contents of the contribu tions fall within the heading of COMPUTATION OF CURVES AND SURFACES and therefore address mathematical and computational issues pertaining to the dis play, modeling, interrogation and representation of complex geometrical objects in various scientific and technical environments. As is the intent of the NATO ASI program the meeting was two weeks in length and the body of the scientific activities was organized around prominent experts. Each of them presented lectures on his current research activity. We were fortunate to have sixteen distinguished invited speakers representing nine NATO countries: W. Bohm (Federal Republic of Germany), C. de Boor (USA), C.K. Chui (USA), W. Dahmen (Federal Republic of Germany), F. Fontanella (Italy), M. Gasca (Spain), R. Goldman (Canada), T.N.T. Goodman (UK), J.A. Gregory (UK), C. Hoffman (USA), J. Hoschek (Federal Republic of Germany), A. Le Mehaute (France), T. Lyche (Norway), C.A. Micchelli (USA), 1.1. Schumaker (USA), C. Traas (The Netherlands). The audience consisted of both young researchers as well as established scientists from twelve NATO countries and several non-NATO countries.
Download or read book Spline Functions on Triangulations written by Ming-Jun Lai and published by Cambridge University Press. This book was released on 2007-04-19 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive graduate text offering a detailed mathematical treatment of polynomial splines on triangulations.
Download or read book Multivariate Splines written by Charles K. Chui and published by SIAM. This book was released on 1988-01-01 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Subject of multivariate splines presented from an elementary point of view; includes many open problems.
Download or read book Approximation and Computation A Festschrift in Honor of Walter Gautschi written by R.V.M. Zahar and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: R. V. M. Zahar* The sixty-fifth birthday of Walter Gautschi provided an opportune moment for an international symposium in his honor, to recognize his many contributions to mathematics and computer sciences. Conceived by John Rice and sponsored by Purdue University, the conference took place in West Lafayette from December 2 to 5, 1993, and was organized around the four main themes representing Professor Gautschi's principal research interests: Approximation, Orthogonal Polynomials, Quadrature and Special Functions. Thirty-eight speakers - colleagues, co-authors, research collaborators or doctoral students of Professor Gautschi - were invited to present articles at the conference, their lectures providing an approximately equal representation of the four disciplines. Five invited speakers, Germund Dahlquist, Philip Davis, Luigi Gatteschi, Werner Rheinboldt and Stephan Ruscheweyh, were unable to present their talks because of illness or other commitments, although Professors Dahlquist, Gatteschi and Ruscheweyh subsequently contributed arti cles to these proceedings. Thus, the final program contained thirty-three technical lectures, ten of which were plenary sessions. Approximately eighty scientists attended the conference, and for some ses sions - in particular, Walter's presentation of his entertaining and informative Reflections and Recollections - that number was complemented by many visitors and friends, as well as the family of the honoree. A surprise visit by Paul Erdos provided one of the highlights of the conference week. The ambiance at the sym posium was extremely collegial, due no doubt to the common academic interests and the personal friendships shared by the participants.
Download or read book A Course in Approximation Theory written by Elliott Ward Cheney and published by American Mathematical Soc.. This book was released on 2009-01-13 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is designed for graduate students in mathematics, physics, engineering, and computer science. Its purpose is to guide the reader in exploring contemporary approximation theory. The emphasis is on multi-variable approximation theory, i.e., the approximation of functions in several variables, as opposed to the classical theory of functions in one variable. Most of the topics in the book, heretofore accessible only through research papers, are treated here from the basics to the currently active research, often motivated by practical problems arising in diverse applications such as science, engineering, geophysics, and business and economics. Among these topics are projections, interpolation paradigms, positive definite functions, interpolation theorems of Schoenberg and Micchelli, tomography, artificial neural networks, wavelets, thin-plate splines, box splines, ridge functions, and convolutions. An important and valuable feature of the book is the bibliography of almost 600 items directing the reader to important books and research papers. There are 438 problems and exercises scattered through the book allowing the student reader to get a better understanding of the subject.
