The Theory of Splines and Their Applications

Author: J. H. Ahlberg
Publisher: Elsevier
ISBN: 1483222950
Format: PDF, Docs
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The Theory of Splines and Their Applications discusses spline theory, the theory of cubic splines, polynomial splines of higher degree, generalized splines, doubly cubic splines, and two-dimensional generalized splines. The book explains the equations of the spline, procedures for applications of the spline, convergence properties, equal-interval splines, and special formulas for numerical differentiation or integration. The text explores the intrinsic properties of cubic splines including the Hilbert space interpretation, transformations defined by a mesh, and some connections with space technology concerning the payload of a rocket. The book also discusses the theory of polynomial splines of odd degree which can be approached through algebraically (which depends primarily on the examination in detail of the linear system of equations defining the spline). The theory can also be approached intrinsically (which exploits the consequences of basic integral relations existing between functions and approximating spline functions). The text also considers the second integral relation, raising the order of convergence, and the limits on the order of convergence. The book will prove useful for mathematicians, physicist, engineers, or academicians in the field of technology and applied mathematics.

Methods of Shape Preserving Spline Approximation

Author: Boris I Kvasov
Publisher: World Scientific
ISBN: 981449447X
Format: PDF, ePub
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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. Contents:Interpolation by Polynomials and Lagrange SplinesCubic Spline InterpolationAlgorithms for Computing 1-D and 2-D Polynomial SplinesMethods of Monotone and Convex Spline InterpolationMethods of Shape-Preserving Spline InterpolationLocal Bases for Generalized Tension SplinesGB-Splines of Arbitrary OrderMethods of Shape Preserving Local Spline ApproximationDifference Method for Construction Hyperbolic Tension SplinesDiscrete Generalized Tension SplinesMethods of Shape Preserving Parametrization Readership: Engineers, physicists, researchers and students in applied mathematics. Keywords:Lagrange Splines;Cubic Splines;Monotone and Convex Spline Interpolation;Shape-Preserving Spline Interpolation;GB-Splines and Recursive Algorithms for GB-Splines;Shape-Preserving Local Spline Approximation;Discrete Generalized Tension Splines;Differential Multipoint Boundary Value Problem;Difference Method for Constructing Hyperbolic Tension Splines;Shape-Preserving ParametrizationReviews: “The book is well written, and I can recommend it to anyone interested in shape-preserving spline methods.” Mathematical Reviews

Approximation and Modeling with B Splines

Author: Klaus HoÓllig
Publisher: SIAM
ISBN: 1611972949
Format: PDF
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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.

Advanced Engineering Materials and Modeling

Author: Ashutosh Tiwari
Publisher: John Wiley & Sons
ISBN: 1119242541
Format: PDF, ePub, Docs
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The engineering of materials with advanced features is driving the research towards the design of innovative materials with high performances. New materials often deliver the best solution for structural applications, precisely contributing towards the finest combination of mechanical properties and low weight. The mimicking of nature's principles lead to a new class of structural materials including biomimetic composites, natural hierarchical materials and smart materials. Meanwhile, computational modeling approaches are the valuable tools complementary to experimental techniques and provide significant information at the microscopic level and explain the properties of materials and their very existence. The modeling also provides useful insights to possible strategies to design and fabricate materials with novel and improved properties. The book brings together these two fascinating areas and offers a comprehensive view of cutting-edge research on materials interfaces and technologies the engineering materials. The topics covered in this book are divided into 2 parts: Engineering of Materials, Characterizations & Applications and Computational Modeling of Materials. The chapters include the following: Mechanical and resistance behavior of structural glass beams Nanocrystalline metal carbides - microstructure characterization SMA-reinforced laminated glass panel Sustainable sugarcane bagasse cellulose for papermaking Electrospun scaffolds for cardiac tissue engineering Bio-inspired composites Density functional theory for studying extended systems First principles based approaches for modeling materials Computer aided materials design Computational materials for stochastic electromagnets Computational methods for thermal analysis of heterogeneous materials Modelling of resistive bilayer structures Modeling tunneling of superluminal photons through Brain Microtubules Computer aided surgical workflow modeling Displaced multiwavelets and splitting algorithms

Random Perturbation Methods with Applications in Science and Engineering

Author: Anatoli V. Skorokhod
Publisher: Springer Science & Business Media
ISBN: 0387224467
Format: PDF, ePub, Mobi
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This book develops methods for describing random dynamical systems, and it illustrats how the methods can be used in a variety of applications. Appeals to researchers and graduate students who require tools to investigate stochastic systems.

Lectures on Constructive Approximation

Author: Volker Michel
Publisher: Springer Science & Business Media
ISBN: 0817684034
Format: PDF
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Lectures on Constructive Approximation: Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball focuses on spherical problems as they occur in the geosciences and medical imaging. It comprises the author’s lectures on classical approximation methods based on orthogonal polynomials and selected modern tools such as splines and wavelets. Methods for approximating functions on the real line are treated first, as they provide the foundations for the methods on the sphere and the ball and are useful for the analysis of time-dependent (spherical) problems. The author then examines the transfer of these spherical methods to problems on the ball, such as the modeling of the Earth’s or the brain’s interior. Specific topics covered include: * the advantages and disadvantages of Fourier, spline, and wavelet methods * theory and numerics of orthogonal polynomials on intervals, spheres, and balls * cubic splines and splines based on reproducing kernels * multiresolution analysis using wavelets and scaling functions This textbook is written for students in mathematics, physics, engineering, and the geosciences who have a basic background in analysis and linear algebra. The work may also be suitable as a self-study resource for researchers in the above-mentioned fields.

Approximation Theory and Spline Functions

Author: S.P. Singh
Publisher: Springer Science & Business Media
ISBN: 9400964668
Format: PDF, ePub, Mobi
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A NATO Advanced Study Institute on Approximation Theory and Spline Functions was held at Memorial University of Newfoundland during August 22-September 2, 1983. This volume consists of the Proceedings of that Institute. These Proceedings include the main invited talks and contributed papers given during the Institute. The aim of these lectures was to bring together Mathematicians, Physicists and Engineers working in the field. The lectures covered a wide range including ~1ultivariate Approximation, Spline Functions, Rational Approximation, Applications of Elliptic Integrals and Functions in the Theory of Approximation, and Pade Approximation. We express our sincere thanks to Professors E. W. Cheney, J. Meinguet, J. M. Phillips and H. Werner, members of the International Advisory Committee. We also extend our thanks to the main speakers and the invi ted speakers, whose contri butions made these Proceedings complete. The Advanced Study Institute was financed by the NATO Scientific Affairs Division. We express our thanks for the generous support. We wish to thank members of the Department of Mathematics and Statistics at MeMorial University who willingly helped with the planning and organizing of the Institute. Special thanks go to Mrs. Mary Pike who helped immensely in the planning and organizing of the Institute, and to Miss Rosalind Genge for her careful and excellent typing of the manuscript of these Proceedings.

Error Inequalities in Polynomial Interpolation and Their Applications

Author: R.P. Agarwal
Publisher: Springer Science & Business Media
ISBN: 9401120269
Format: PDF, Docs
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This volume, which presents the cumulation of the authors' research in the field, deals with Lidstone, Hermite, Abel--Gontscharoff, Birkhoff, piecewise Hermite and Lidstone, spline and Lidstone--spline interpolating problems. Explicit representations of the interpolating polynomials and associated error functions are given, as well as explicit error inequalities in various norms. Numerical illustrations are provided of the importance and sharpness of the various results obtained. Also demonstrated are the significance of these results in the theory of ordinary differential equations such as maximum principles, boundary value problems, oscillation theory, disconjugacy and disfocality. For mathematicians, numerical analysts, computer scientists and engineers.