Splines and PDEs: From Approximation Theory to Numerical Linear Algebra - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Splines and PDEs: From Approximation Theory to Numerical Linear Algebra write by Angela Kunoth. This book was released on 2018-09-20. Splines and PDEs: From Approximation Theory to Numerical Linear Algebra available in PDF, EPUB and Kindle. This book takes readers on a multi-perspective tour through state-of-the-art mathematical developments related to the numerical treatment of PDEs based on splines, and in particular isogeometric methods. A wide variety of research topics are covered, ranging from approximation theory to structured numerical linear algebra. More precisely, the book provides (i) a self-contained introduction to B-splines, with special focus on approximation and hierarchical refinement, (ii) a broad survey of numerical schemes for control problems based on B-splines and B-spline-type wavelets, (iii) an exhaustive description of methods for computing and analyzing the spectral distribution of discretization matrices, and (iv) a detailed overview of the mathematical and implementational aspects of isogeometric analysis. The text is the outcome of a C.I.M.E. summer school held in Cetraro (Italy), July 2017, featuring four prominent lecturers with different theoretical and application perspectives. The book may serve both as a reference and an entry point into further research.
Approximation by Spline Functions
Approximation by Spline Functions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Approximation by Spline Functions write by Günther Nürnberger. This book was released on 1989-11-16. Approximation by Spline Functions available 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.
Approximation and Modeling with B-Splines
Approximation and Modeling with B-Splines - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Approximation and Modeling with B-Splines write by Klaus Hollig. This book was released on 2015-07-01. Approximation and Modeling with B-Splines available in PDF, EPUB and Kindle. B-splines are fundamental to approximation and data fitting, geometric modeling, automated manufacturing, computer graphics, and numerical simulation. With an emphasis on key results and methods that are most widely used in practice, this textbook provides a unified introduction to the basic components of B-spline theory: approximation methods (mathematics), modeling techniques (engineering), and geometric algorithms (computer science). A supplemental Web site will provide a collection of problems, some with solutions, slides for use in lectures, and programs with demos.
Splines and Variational Methods
Splines and Variational Methods - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Splines and Variational Methods write by P. M. Prenter. This book was released on 2013-11-26. Splines and Variational Methods available in PDF, EPUB and Kindle. One of the clearest available introductions to variational methods, this text requires only a minimal background in calculus and linear algebra. Its self-contained treatment explains the application of theoretic notions to the kinds of physical problems that engineers regularly encounter. The text’s first half concerns approximation theoretic notions, exploring the theory and computation of one- and two-dimensional polynomial and other spline functions. Later chapters examine variational methods in the solution of operator equations, focusing on boundary value problems in one and two dimensions. Additional topics include least squares and other Galerkin methods. Many helpful definitions, examples, and exercises appear throughout the book. A classic reference in spline theory, this volume will benefit experts as well as students of engineering and mathematics.
Mathematical and Computational Methods for Modelling, Approximation and Simulation
Mathematical and Computational Methods for Modelling, Approximation and Simulation - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Mathematical and Computational Methods for Modelling, Approximation and Simulation write by Domingo Barrera. This book was released on 2022-05-08. Mathematical and Computational Methods for Modelling, Approximation and Simulation available in PDF, EPUB and Kindle. This book contains plenary lectures given at the International Conference on Mathematical and Computational Modeling, Approximation and Simulation, dealing with three very different problems: reduction of Runge and Gibbs phenomena, difficulties arising when studying models that depend on the highly nonlinear behaviour of a system of PDEs, and data fitting with truncated hierarchical B-splines for the adaptive reconstruction of industrial models. The book includes nine contributions, mostly related to quasi-interpolation. This is a topic that continues to register a high level of interest, both for those working in the field of approximation theory and for those interested in its use in a practical context. Two chapters address the construction of quasi-interpolants, and three others focus on the use of quasi-interpolation in solving integral equations. The remaining four concern a problem related to the heat diffusion equation, new results on the notion of convexity in probabilistic metric spaces (which are applied to the study of the existence and uniqueness of the solution of a Volterra equation), the use of smoothing splines to address an economic problem and, finally, the analysis of poverty measures, which is a topic of increased interest to society. The book is addressed to researchers interested in Applied Mathematics, with particular reference to the aforementioned topics.
