The Magnus series is an infinite series which arises in the study of linear ordinary differential equations. If the series converges, then the matrix exponential of the sum equals...
We introduce some modifications and extensions of the concept od index pair in the Conley index theory. We then show how these concepts may be used to overcome some difficulties in...
We present an approach that allows performing computations related to the Baker-Campbell-Haussdorff (BCH) formula and its generalizations in an arbitrary Hall basis, using labeled...
This paper considers the regularized learning algorithm associated with the leastsquare loss and reproducing kernel Hilbert spaces. The target is the error analysis for the regres...
The main result of this paper is a new version of Newton-Hensel lifting that relates to interpolation questions. It allows one to lift polynomials in Z[x] from information modulo a...
In this paper, we study an online learning algorithm in Reproducing Kernel Hilbert Spaces (RKHS) and general Hilbert spaces. We present a general form of the stochastic gradient m...
We study the algebraic and facial structures of hyperbolic programs, and examine natural relaxations of hyperbolic programs, the relaxations themselves being hyperbolic programs.