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Ming-Jun Lai And Larry L. Schumaker Listings

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1 Ming-Jun Lai and Larry L. Schumaker
Spline Functions on Triangulations: Encyclopedia of Mathematics and Its Applications 110
Cambridge University Press; Cambridge, UK; 2007; 978052187529; First Edition; Hard Cover; New; New; 
Spline functions are universally recognized as highly effective tools in approximation theory, computer-aided geometric design, image analysis, and numerical analysis. The theory of univariate splines is well known but this text is the first comprehensive treatment of the analogous bivariate theory. A detailed mathematical treatment of polynomial splines on triangulations is outlined, providing a basis for developing practical methods for using splines in numerous application areas. The detailed treatment of the Bernstein-Bézier representation of polynomials will provide a valuable source for researchers and students in CAGD. Chapters on smooth macro-element spaces will allow engineers and scientists using the FEM method to solve partial differential equations numerically with new tools. Workers in the geosciences will find new tools for approximation and data fitting on the sphere. Ideal as a graduate text in approximation theory, and as a source book for courses in computer-aided geometric design or in finite-element methods. • First book to offer a detailed treatment of bivariate splines • Provides a basis for developing practical methods for using splines in numerous application areas • Up-to-date and comprehensive account, suitable for mathematicians, statisticians, engineers, geoscientists, biologists and computer scientists working in academia or industry Contents Preface; 1. Bivariate polynomials; 2. Bernstein-Bézier methods for bivariate polynomials; 3. B-patches; 4. Triangulations and quadrangulations; 5. Bernstein-Bézier methods for spline spaces; 6. C1 Macro-element spaces; 7. C2 Macro-element spaces; 8. Cr Macro-element spaces; 9. Dimension of spline splines; 10. Approximation power of spline spaces; 11. Stable local minimal determining sets; 12. Bivariate box splines; 13. Spherical splines; 14. Approximation power of spherical splines; 15. Trivariate polynomials; 16. Tetrahedral partitions; 17. Trivariate splines; 18. Trivariate macro-element spaces; Bibliography; Index. Printed Pages: 608 with 83 line diagrams, 32 half-tones, 12 tables, and 41 worked examples. 019784

Price: 125.00 USD
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