Career
- 2000-present: University Lecturer, DAMTP, University of Cambridge
- 1997-2000: Research Assistant, RWTH Aachen, Germany
- 1995-1997: Alexander von Humboldt Fellow, University of Bonn, Germany
- 1986-1995: Research Scientist, Novosibirsk Computing Center, Russia
Research
Alexei Shadrin is a Lecturer at DAMTP and a member of the Numerical Analysis and Computational Mathematics Group therein. His area of interests lies within Approximation Theory and includes, more specifically, various aspects of spline and polynomial interpolation, shape-preserving approximation, Markov- and Landau-Kolmogorov-type inequalities between derivatives (which are, in short, the problems of numerical differentiation). His current research topics are Karlin's conjecture, Zolotarev polynomials and exact constants in the Jackson-Stechkin-type inequalities.
Selected Publications
- S. Foucart, Y. Kryakin, A. Shadrin, On the exact constant in the Jackson-Stechkin inequality for the uniform metric, Constr. Approx. 29 (2009), 157-179.
- A. Shadrin, Twelve proofs of the Markov inequality, in: Approximation Theory: a volume dedicated to Borislav Bojanov, Prof. Drinov Acad. Publ. House, Sofia, 2004, 233-298.
- K. Kopotun, A. Shadrin, On k-monotone approximation by free-knot splines, SIAM J. Math. Anal. 34 (2003), 901-924.
- A. Yu. 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 (2001), 59-137.
- K. Scherer, A. Shadrin, New upper bound for the B-spline basis condition number. II. A proof of de Boor's 2^k-conjecture, J. Approx. Theory 99 (1999), 217-229.
- A. Shadrin, Error bounds for Lagrange interpolation, J. Approx. Theory 80 (1995), 25-49.
Publications
On k-monotone approximation by free knot splines
– SIAM Journal on Mathematical Analysis
(2006)
34,
901
(DOI: 10.1137/s0036141002358514)
The L∞-norm of the L2-spline projector is bounded independently of the knot sequence: A proof of de Boor's conjecture
– Acta Mathematica
(2001)
187,
59
(DOI: 10.1007/bf02392832)
New Upper Bound for the B-Spline Basis Condition Number
– Journal of Approximation Theory
(1999)
99,
217
(DOI: 10.1006/jath.1998.3310)
Error Bounds for Lagrange Interpolation
– Journal of Approximation Theory
(1995)
80,
25
(DOI: 10.1006/jath.1995.1003)
Letter to the editor about A. I. Zvyagintsev's paper “Extremal problem on the norm of an intermediate derivative”
– Mathematical Notes
(1994)
55,
543
(DOI: 10.1007/bf02110383)
Interpolation by Lagrange polynomials, B-splines and bounds of errors
– Analysis Mathematica
(1994)
20,
213
(DOI: 10.1007/BF01924094)
On L_{p}-Boundedness of the L_{2}-Projector onto Splines
– Journal of Approximation Theory
(1994)
77,
331
(DOI: 10.1006/jath.1994.1054)
Interpolation by lagrange polynomials and sharp constants in inequalities for the norms of derivatives on a finite segment
– Mathematical Notes
(1993)
54,
1165
(DOI: 10.1007/bf01208398)
Interpolation with lagrange polynomials a simple proof of Markov inequality and some of its generalizations
– Analysis in Theory and Applications
(1992)
8,
51
(DOI: 10.1007/BF02836338)
Inequalities of Kolmogorov type and estimates of spline interpolation on periodic classes W_{2}^{m}
– Mathematical Notes of the Academy of Sciences of the USSR
(1990)
48,
1058
(DOI: 10.1007/bf01139609)
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