Related papers: Reminiscences about numerical schemes
This is a PhD dissertation on the latest numerical quantum estimation schemes as of 2012, submitted to the National University of Singapore. The main content of the thesis focuses on accessing quantum information with informationally…
Lecture notes (in French) of a master 2 level course in applied mathematics. Contents: Part I. Markov chains on a countable space. 1. Examples 2. Summary of basic properties. 3. Spectral theory and speed of convergence. 4. Lyapunov…
After carefully checking the original Russian version of Kolmogorov (1942), in the present author view, both Spalding and Wilcox misinterpretations are due to the fact that they did not notice the two different symbols, which Kolmogorov…
First-order methods are often analyzed via their continuous-time models, where their worst-case convergence properties are usually approached via Lyapunov functions. In this work, we provide a systematic and principled approach to find and…
This is expanded text of a lecture delivered by the author at the conference "Mat\'eriaux pour l'Histoire des Math\'ematiques au XX\`eme si\`ecle", which took place in Nice in January 1996. The task was to describe one area in the…
In his 1685 paper "Observationes cyclometricae" published in Acta Eruditorum, Adam Adamandy Kocha\'nski presented an approximate ruler-and-compass construction for rectification of the circle. It is not generally known that the first part…
This is a collection of open problems in Group Theory proposed by more than 300 mathematicians from all over the world. It has been published every 2-4 years in Novosibirsk since 1965, now also in English. This is the 18th Russian edition,…
We discuss some mistakes and curiosities concerned with the celebrated First International Topological Conference in Moscow, 1935.
The drawbacks in the formulations of random infinite divisibility in Sandhya (1991, 1996), Gnedenko and Korelev (1996), Klebanov and Rachev (1996), Bunge (1996) and Kozubowski and Panorska (1996) are pointed out. For any given Laplace…
Markov's inequality for algebraic polynomials on $\left[-1,1\right]$ goes back to more than a century and it is widely used in approximation theory. Its asymptotically sharp form for unions of finitely many intervals has been found only in…
This is a survey (21 pages, 124 references) written for the MCQMC 2014 conference in Leuven, April 2014. We start with the seminal paper of Bakhvalov (1959) and end with new results on the curse of dimension and on the complexity of…
This paper focuses on providing the computation methods for the backward time tempered fractional Feynman-Kac equation, being one of the models recently proposed in [Wu, Deng, and Barkai, Phys. Rev. E, 84 (2016) 032151]. The discretization…
The low-dissipation central-upwind (LDCU) schemes have been recently introduced in [A. Kurganov and R. Xin, J. Sci. Comput., 96 (2023), Paper No. 56] as a modification of the central-upwind (CU) schemes from [{\sc A. Kurganov and C. T. Lin,…
We consider a splitting approach for the Kadomtsev--Petviashvili equation with periodic boundary conditions and show that the necessary interpolation procedure can be efficiently implemented. The error made by this numerical scheme is…
Central schemes are frequently used for incompressible and compressible flow calculations. The present paper is the first in a forthcoming series where a new approach to a 2nd order accurate Finite Volume scheme operating on cartesian grids…
PhD Thesis under the supervision of Professor Nedyalko Nenov.
The aim of this chapter is twofold. In the first part we will provide a brief overview of the mathematical and statistical foundations of graphical models, along with their fundamental properties, estimation and basic inference procedures.…
This is a detailed answer to the criticism of my paper.
A particular case of initial data for the two-dimensional Euler equations is studied numerically. The results show that the Godunov method does not always converge to the physical solution, at least not on feasible grids. Moreover, they…
The article is devoted to introduce and investigation of new numeral systems. These representations are generalizations of classical representations of real numbers. The main properties of investigating representations are described. The…