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| Detailed information |
| Original study plan |
Bachelor's programme Technical Mathematics 2009W |
| Objectives |
Conveying of important topics in the theory of splines
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| Subject |
Kapitel 1. Introduction
Kapitel 2. Prologue
- Best Approximation
- Interpolation of functions
- Divided Differences
- Total Positivity of Matrices
Kapitel 3. Polynomial functions
- Defintions
- Inequalities of Bernstein, Szegö and Markov
- Lp -Norms of polynomials
- Degree of Approximation of Polynomials
Kapitel 4. 1D Spline functions
- piecewise linear functions
- piecewise polynomials
- B-Splines
- Dual Funktionals to B-Splines
- Degree of Approximation of Spline functions
- Refining knot sequences
- Collocation
Kapitel 5. Higher dimenional spline functions
- Definitions and simple properties
- Recursion formulae
- Examples
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| Criteria for evaluation |
Oral exam at the end of the semester
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| Methods |
Blackboard talk combined with lecture notes
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| Language |
German |
| Study material |
[1] H. B. Curry and I. J. Schoenberg. On Pólya frequency functions. IV. The fundamental spline functions and their limits. J. Analyse Math., 17:71–107, 1966.
[2] C. de Boor. Splinefunktionen. Lectures in Mathematics ETH Zürich. Birkhäuser Verlag, Basel, 1990.
[3] S. Demko. Inverses of band matrices and local convergence of spline projections. SIAM J. Numer. Anal., 14(4):616–619, 1977.
[4] R. A. DeVore and G. G. Lorentz. Constructive approximation, volume 303 of Grundlehren der Mathematischen Wissenschaften. Springer-Verlag, Berlin,1993.
[5] L. L. Schumaker. Spline functions: basic theory. Cambridge Mathematical Library. Cambridge University
[6] A. Y. Shadrin. The L∞ -norm of the L2 -spline projector is bounded independently of the knot sequence:
a proof of de Boor’s conjecture. Acta Math., 187(1):59–137, 2001.
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| Changing subject? |
No |
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