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
Sampling discretization of integral norms.
– CoRR
(2020)
abs/2001.09320,
Optimal sampling rates for approximating analytic functions from pointwise samples
– IMA Journal of Numerical Analysis
(2018)
39,
1360
(DOI: 10.1093/imanum/dry024)
On the largest critical value of Tnk
– SIAM Journal on Mathematical Analysis
(2018)
50,
2389
(DOI: 10.1137/17M1152413)
On the Largest Critical Value of $T_n^(k)$
– SIAM J. Math. Anal.
(2018)
50,
2389
(DOI: 10.1137/17m1152413)
On the Markov inequality in the $L_2$-norm with the Gegenbauer weight
– Constructive Approximation
(2017)
49,
1
(DOI: 10.1007/s00365-017-9406-2)
On the $L_2$ Markov Inequality with Laguerre Weight
(2017)
117,
1
(DOI: 10.1007/978-3-319-49242-1_1)
On the Markov inequality in the $L_2$-norm with Gegenbauer weight
– Journal of Approximation Theory
(2016)
208,
9
(DOI: 10.1016/j.jat.2016.03.005)
On almost everywhere convergence of orthogonal spline projections with arbitrary knots
– Journal of Approximation Theory
(2014)
180,
77
(DOI: 10.1016/j.jat.2013.12.004)
A Stability Barrier for Reconstructions from Fourier Samples.
– SIAM J. Numer. Anal.
(2014)
52,
125
(DOI: 10.1137/130908221)
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