Splines and Variational Methods
Splines and Variational Methods

Author: P. M. Prenter

Publisher: Courier Corporation

Published: 2013-11-26

Total Pages: 338

ISBN-13: 0486783499

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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.

Splines and Variational Methods
Splines and Variational Methods

Author: P. M. Prenter

Publisher: Courier Corporation

Published: 2008-01-01

Total Pages: 338

ISBN-13: 0486469026

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One of the clearest available introductions to variational methods, this text requires only a minimal background in linear algebra and analysis. It explains the application of theoretic notions to the kinds of physical problems that engineers regularly encounter. Many helpful definitions, examples, and exercises appear throughout the book. 1975 edition.

Finite Element Methods with B-splines
Finite Element Methods with B-splines

Author: Klaus Hollig

Publisher: SIAM

Published: 2003-01-01

Total Pages: 155

ISBN-13: 9780898717532

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Finite Element Methods with B-Splines describes new weighted approximation techniques, combining the computational advantages of B-splines and standard finite elements. In particular, no grid generation is necessary, which eliminates a difficult and often time-consuming preprocessing step. The meshless methods are very efficient and yield highly accurate solutions with relatively few parameters. This is illustrated for typical boundary value problems in fluid flow, heat conduction, and elasticity. Topics discussed by the author include basic finite element theory, algorithms for B-splines, weighted bases, stability and error estimates, multigrid techniques, applications, and numerical examples.

Spline Models for Observational Data
Spline Models for Observational Data

Author: Grace Wahba

Publisher: SIAM

Published: 1990-09-01

Total Pages: 174

ISBN-13: 0898712440

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This book serves well as an introduction into the more theoretical aspects of the use of spline models. It develops a theory and practice for the estimation of functions from noisy data on functionals. The simplest example is the estimation of a smooth curve, given noisy observations on a finite number of its values. Convergence properties, data based smoothing parameter selection, confidence intervals, and numerical methods are established which are appropriate to a number of problems within this framework. Methods for including side conditions and other prior information in solving ill posed inverse problems are provided. Data which involves samples of random variables with Gaussian, Poisson, binomial, and other distributions are treated in a unified optimization context. Experimental design questions, i.e., which functionals should be observed, are studied in a general context. Extensions to distributed parameter system identification problems are made by considering implicitly defined functionals.

Multidimensional Minimizing Splines
Multidimensional Minimizing Splines

Author: R. Arcangéli

Publisher: Springer Science & Business Media

Published: 2004-06-24

Total Pages: 267

ISBN-13: 1402077866

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This book is of interest to mathematicians, geologists, engineers and, in general, researchers and post graduate students involved in spline function theory, surface fitting problems or variational methods. From reviews: The book is well organized, and the English is very good. I recommend the book to researchers in approximation theory, and to anyone interested in bivariate data fitting." (L.L. Schumaker, Mathematical Reviews, 2005).

Advanced Finite Element Method in Structural Engineering
Advanced Finite Element Method in Structural Engineering

Author: Yu-Qiu Long

Publisher: Springer Science & Business Media

Published: 2009-09-29

Total Pages: 715

ISBN-13: 3642003168

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Advanced Finite Element Method in Structural Engineering systematically introduces the research work on the Finite Element Method (FEM), which was completed by Prof. Yu-qiu Long and his research group in the past 25 years. Seven original theoretical achievements - for instance, the Generalized Conforming Element method, to name one - and their applications in the fields of structural engineering and computational mechanics are discussed in detail. The book also shows the new strategies for avoiding five difficulties that exist in traditional FEM (shear-locking problem of thick plate elements; sensitivity problem to mesh distortion; non-convergence problem of non-conforming elements; accuracy loss problem of stress solutions by displacement-based elements; stress singular point problem) by utilizing foregoing achievements.

Spline Functions: Basic Theory
Spline Functions: Basic Theory

Author: Larry Schumaker

Publisher: Cambridge University Press

Published: 2007-08-16

Total Pages: 524

ISBN-13: 1139463438

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This classic work continues to offer a comprehensive treatment of the theory of univariate and tensor-product splines. It will be of interest to researchers and students working in applied analysis, numerical analysis, computer science, and engineering. The material covered provides the reader with the necessary tools for understanding the many applications of splines in such diverse areas as approximation theory, computer-aided geometric design, curve and surface design and fitting, image processing, numerical solution of differential equations, and increasingly in business and the biosciences. This new edition includes a supplement outlining some of the major advances in the theory since 1981, and some 250 new references. It can be used as the main or supplementary text for courses in splines, approximation theory or numerical analysis.

Computational Mechanics in Structural Engineering
Computational Mechanics in Structural Engineering

Author: F.Y. Cheng

Publisher: CRC Press

Published: 2003-10-04

Total Pages: 481

ISBN-13: 1482296691

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Proceedings of Sino-US Joint Symposium/Workshop on Recent Developments and Future Trends of Computational Mechanics in Structural Engineering, Beijing, China, September 24-28 1991