6 papers
A sharp estimate of the discrepancy of a certain numerical sequence
Martin Lind
We consider a certain equidistributed sequence of rational numbers constructed from the primes. In particular, we determine the sharp convergence rate for the star discrepancy of s…
The modulus of -variation and its applications
Gholam Hossein Esslamzadeh, Milad Moazami Goodarzi, Mahdi Hormozi +1
In this note, we introduce the notion of modulus of -variation for a function of a real variable, and show that it serves in at least two important problems, namely, the uniform…
An extension of Koksma's inequality
Martin Lind
When applying the quasi-Monte Carlo (QMC) method of numerical integration of univariate functions, Koksma's inequality provides a basic estimate of the error in terms of the discre…
A semidiscrete Galerkin scheme for a coupled two-scale elliptic-parabolic system: well-posedness and convergence approximation rates
Martin Lind, Adrian Muntean, Omar Richardson
In this paper, we study the numerical approximation of a coupled system of elliptic-parabolic equations posed on two separated spatial scales. The model equations describe the inte…
Nonlinear nonnested 2-D spline approximation
Martin Lind, Pencho Petrushev
Nonlinear approximation from regular piecewise polynomials (splines) of degree supported on rings in is studied. By definition a ring is a set in obtained by sub…
On embeddings of spaces of bivariate functions of bounded -variation
Martin Lind
We obtain sharp estimates of the Hardy-Vitali type total -variation of a function of two variables in terms of its mixed modulus of continuity in . We also investi…