Download or read book Fast Compact Algorithms and Software for Spline Smoothing written by Howard L. Weinert and published by Springer Science & Business Media. This book was released on 2012-10-11 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fast Compact Algorithms and Software for Spline Smoothing investigates algorithmic alternatives for computing cubic smoothing splines when the amount of smoothing is determined automatically by minimizing the generalized cross-validation score. These algorithms are based on Cholesky factorization, QR factorization, or the fast Fourier transform. All algorithms are implemented in MATLAB and are compared based on speed, memory use, and accuracy. An overall best algorithm is identified, which allows very large data sets to be processed quickly on a personal computer.
Download or read book Spline Functions written by Larry L. Schumaker and published by SIAM. This book was released on 2015-01-01 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes in detail the key algorithms needed for computing with spline functions and illustrates their use in solving several basic problems in numerical analysis, including function approximation, numerical quadrature, data fitting, and the numerical solution of PDE's. The focus is on computational methods for bivariate splines on triangulations in the plane and on the sphere, although both univariate and tensor-product splines are also discussed. The book contains numerous examples and figures to illustrate the methods and their performance. All of the algorithms in the book have been coded in a separate MATLAB package available for license. The package can be used to run all of the examples in the book and also provides readers with the essential tools needed to create software for their own applications. In addition to the included bibliography, a list of over 100 pages of additional references can be found on the book's website.
Download or read book A New Algorithm for Spline Smoothing Based on Smoothing a Stochastic Process written by Robert Kohn and published by . This book was released on 1985 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Smoothing Splines written by Yuedong Wang and published by CRC Press. This book was released on 2011-06-22 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Curve and Surface Fitting with Splines written by Paul Dierckx and published by Oxford University Press. This book was released on 1995 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fitting of a curve or surface through a set of observational data is a very frequent problem in different disciplines (mathematics, engineering, medicine, ...) with many interesting applications. This book describes the algorithms and mathematical fundamentals of a widely used software package for data fitting with (tensor product) splines. As such it gives a survey of possibilities and benefits but also of the problems to cope with when approximating with this popular type of function. In particular it is demonstrated in detail how the properties of B-splines can be fully exploited for improving the computational efficiency and for incorporating different boundary or shape preserving constraints. Special attention is also paid to strategies for an automatic and adaptive knot selection with intent to obtain serious data reductions. The practical use of the smoothing software is illustrated with many examples, academic as well as taken from real life.
Download or read book An Algorithm for Surface Smoothing with Rational Splines written by James R. Schiess and published by . This book was released on 1987 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Topics in Bivariate Spline Smoothing written by Luo Xiao and published by . This book was released on 2012 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: Penalized spline methods have been popular since the work of Eilers and Marx (1996). Recent years saw extensive theoretical studies and a wide range of applications of penalized splines. In this dissertation, we consider penalized splines for smoothing two-dimensional data. In Chapter 2, we propose a new spline smoother, the sandwich smoother, for smoothing data on a rectangular grid. Univariate P-spline smoothers are applied simultaneously along both coordinates. The sandwich smoother has a tensor product structure that simplifies an asymptotic analysis and it can be fast computed. We derive a local central limit theorem for the sandwich smoother, with simple expressions for the asymptotic bias and variance, by showing that the sandwich smoother is asymptotically equivalent to a bivariate kernel regression estimator with a product kernel. As far as we are aware, this is the first central limit theorem for a bivariate spline estimator of any type. Our simulation study shows that the sandwich smoother is orders of magnitude faster to compute than other bivariate spline smoothers, even when the latter are computed using a fast GLAM (Generalized Linear Array Model) algorithm, and comparable to them in terms of mean squared integrated errors. One important application of the sandwich smoother is to estimate covariance functions in functional data analysis. In this application, our numerical results show that the sandwich smoother is orders of magnitude faster than local linear regression. In Chapter 3, based on the sandwich smoother, we propose a fast covariance function estimation method (FACE) for smoothing high-dimensional functional data. We show that our method overcomes the computational difficulty of common bivariate smoothers for smoothing high-dimensional covariance operators, and in particular we derive a fast algorithm for selecting the smoothing parameter. We also show that through FACE we can simultaneously obtain the smoothed covariance operator and its associated eigenfunctions. For functional principal component analysis, we derive a fast method for calculating the principal scores. A simulation study is done to illustrate the computational speed of FACE. Although not a focus of this dissertation, we present in Appendix A a theoretical study of the local asymptotics of P-splines for the univariate case. In this work we derived the local asymptotic distribution of P-splines at both an interior point and near the boundary. Some of the results in the work are used in studying the sandwich smoother.
Download or read book Fast Algorithms for Smoothing Data Over a Disc Or a Sphere Using Tensor Product Splines written by P. Dierckx and published by . This book was released on 1985 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Smoothing Algorithm Using Cubic Spline Functions written by Robert Lee Smith and published by . This book was released on 1974 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algorithms for Approximation written by J.C. Mason and published by Chapman and Hall/CRC. This book was released on 1990-05-15 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises the proceedings of the second Shrivenham conference on Algorithms for Approximation. The term 'approximation' here refers to 'the approximation of functions and data by similar functions', and leads to such topics as curve and surface fitting, spline and piecewise polynomial methods, finite element modelling, and computer-aided design. Applications are given to a wide variety of areas such as surveying, meteorology, radar antenna and acoustic array design, topography, engineering metrology, and CAD/CAM. Emphasis at the meeting was placed on the development of useful algorithms, and on practical applications in defence and industry. In addition, some 40 submitted papers were selected and presented on a multitude of topics such as multivariate interpolation, optimization methods, constrained problems, spline fitting, data modelling, and applications in microwave measurement, isotropic antennas, sound measurement, and digitized contours.
Download or read book A New Algorithm for Spline Smoothing and Interpolation Based on Smoothing a Stochastic Process written by Robert Kohn and published by . This book was released on 1984 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spline Smoothing by Generalized Cross validation written by P. H. Merz and published by . This book was released on 1982 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Comprehensive Materials Processing written by and published by Newnes. This book was released on 2014-04-07 with total page 5485 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive Materials Processing, Thirteen Volume Set provides students and professionals with a one-stop resource consolidating and enhancing the literature of the materials processing and manufacturing universe. It provides authoritative analysis of all processes, technologies, and techniques for converting industrial materials from a raw state into finished parts or products. Assisting scientists and engineers in the selection, design, and use of materials, whether in the lab or in industry, it matches the adaptive complexity of emergent materials and processing technologies. Extensive traditional article-level academic discussion of core theories and applications is supplemented by applied case studies and advanced multimedia features. Coverage encompasses the general categories of solidification, powder, deposition, and deformation processing, and includes discussion on plant and tool design, analysis and characterization of processing techniques, high-temperatures studies, and the influence of process scale on component characteristics and behavior. Authored and reviewed by world-class academic and industrial specialists in each subject field Practical tools such as integrated case studies, user-defined process schemata, and multimedia modeling and functionality Maximizes research efficiency by collating the most important and established information in one place with integrated applets linking to relevant outside sources
Download or read book A Fast Algorithm for Smoothing Data on a Rectangular Grid While Using Spline Functions written by P. Dierckx and published by . This book was released on 1980 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Directory of Computer Software Applications written by and published by . This book was released on 1979 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Electrical Electronics Abstracts written by and published by . This book was released on 1997 with total page 2240 pages. Available in PDF, EPUB and Kindle. Book excerpt:
