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# Department of Applied Mathematics and Theoretical Physics

## 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.
F Dai, A Prymak, A Shadrin, V Temlyakov, S Tikhonov
– CoRR
(2020)
abs/2001.09320,
Optimal sampling rates for approximating analytic functions from pointwise samples
B Adcock, RB Platte, A Shadrin
– IMA Journal of Numerical Analysis
(2018)
39,
1360
On the Largest Critical Value of $T_n^(k)$
N Naidenov, G Nikolov, A Shadrin
– SIAM Journal on Mathematical Analysis
(2018)
50,
2389
On the largest critical value of Tnk
N Naidenov, G Nikolov, A Shadrin
– SIAM Journal on Mathematical Analysis
(2018)
50,
2389
On the Markov inequality in the $L_2$-norm with the Gegenbauer weight
G Nikolov, A Shadrin
– Constructive Approximation
(2017)
49,
1
On the $L_2$ Markov Inequality with Laguerre Weight
G Nikolov, A Shadrin
(2017)
117,
1
On the L2 markov inequality with laguerre weight
G Nikolov, A Shadrin
(2017)
117,
1
On the Markov inequality in the $L_2$-norm with Gegenbauer weight
D Aleksov, G Nikolov, A Shadrin
– J. Approx. Theory
(2016)
208,
9
On almost everywhere convergence of orthogonal spline projections with arbitrary knots.
M Passenbrunner, A Shadrin
– Journal of Approximation Theory
(2014)
180,
77
A Stability Barrier for Reconstructions from Fourier Samples
B Adcock, AC Hansen, A Shadrin
– SIAM Journal on Numerical Analysis
(2014)
52,
125
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## Research Groups

Cantab Capital Institute for the Mathematics of Information
Numerical Analysis

F2.03

01223 766887