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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

On k-Monotone Approximation by Free Knot Splines
K Kopotun, A Shadrin
– SIAM J. Math. Anal.
(2006)
34,
901
TheL∞-norm of theL2-spline projector is bounded independently of the knot sequence: A proof of de Boor's conjecture
AY Shadrin
– Acta Mathematica
(2001)
187,
59
New Upper Bound for the B-Spline Basis Condition Number
K Scherer, AY Shadrin
– Journal of Approximation Theory
(1999)
99,
217
Error Bounds for Lagrange Interpolation
A SHADRIN
– Journal of Approximation Theory
(1995)
80,
25
Letter to the editor about A. I. Zvyagintsev's paper “Extremal problem on the norm of an intermediate derivative”
AY Shadrin
– Mathematical Notes
(1994)
55,
543
Interpolation by Lagrange polynomials, B-splines and bounds of errors
AU shADRIN
– Analysis Mathematica
(1994)
20,
213
On Lp-Boundedness of the L2-Projector onto Splines
A SHADRIN
– Journal of Approximation Theory
(1994)
77,
331
Interpolation by lagrange polynomials and sharp constants in inequalities for the norms of derivatives on a finite segment
AY Shadrin
– Mathematical Notes
(1993)
54,
1165
Interpolation with lagrange polynomials a simple proof of Markov inequality and some of its generalizations
A Shadrin
– Analysis in Theory and Applications
(1992)
8,
51
Inequalities of Kolmogorov type and estimates of spline interpolation on periodic classes W2m
AY Shadrin
– Mathematical Notes of the Academy of Sciences of the USSR
(1990)
48,
1058
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Research Groups

Cantab Capital Institute for the Mathematics of Information
Numerical Analysis

Room

F2.03

Telephone

01223 766887