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| Detailed information |
| Original study plan |
Bachelor's programme Technical Mathematics 2025W |
| Learning Outcomes |
Competences |
| Students know simple concepts of approximation theory and
their connection to polynomials and spline functions
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| Skills |
Knowledge |
- Know simple methods of approximation theory and use them to investigate spline spaces
- Understand proofs of polynomial inequalities and use them in applications
- Define (B-)spline functions and work with their properties
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Best approximation, divided differences, total positivity of
matrices, Bernstein and Markov inequalities, degree of approximation of
polynomial functions, piecewise polynomial functions, B-splines, degree of
approximation of spline functions, refinement of the knot sequence, spline
collocation, multivariate spline functions
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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 |
English and French |
| 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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