UNION OF BULGARIAN MATHEMATICIANS
INSTITUTE OF MATHEMATICS AND INFORMATICS, BULGARIAN ACADEMY OF SCIENCES

NATIONAL MATHEMATICS COLLOQUIUM

The next meeting of the National Mathematics Colloquium will be held on June 27, 2018 (Уеахеяаьщ) at 16:00 in the Conference Room of the Institute of Mathematics and Informatics, Acad. G. Bonchev Street, Block 8

A talk on:

On stable reconstruction from Fourier coefficients

will be delivered by Acad. Sergey Konyagin from the Steklov Mathematics Institute, Moscow, Russian Academy of Sciences.

Everybody is invited.

Head of the Colloquium: Acad. P. Popivanov

Abstract. B. Adcock, A. S. Hansen and A. Shadrin proved that any stable method for recovering high-order accuracy from the first m Fourier coefficients of an analytic and nonperiodic function can converge at best root-exponentially fast in m. Any method with faster convergence must also be unstable, and in particular, exponential convergence implies exponential ill-conditioning. Shadrin asked about possible benefit if we take m arbitrary Fourier coefficients. We show that this cannot improve the convergence of stable methods for recovering. However, we can hope to have exponential convergence with polynomial ill-conditioning.