Small Oscillations to any Degree of Approximation

Diophantine Approximation in Small Degree

Here, the exponent of q in the upper bound is optimal because, when ξ has bounded partial quotients, there is also a constant c > 0 such that |ξ − p/q| ≥ cq for all rational numbers p/q (see Chapter I of [14]). Define the height H(P ) of a polynomial P ∈ R[T ] as the largest absolute value of its coefficients, and the height H(α) of an algebraic number α as the height of its irreducible polynom...

Non-uniform spline recovery from small degree polynomial approximation

We investigate the sparse spikes deconvolution problem onto spaces of algebraic polynomials. Our framework encompasses the measure reconstruction problem from a combination of noiseless and noisy moment measurements. We study a TV-norm regularization procedure to localize the support and estimate the weights of a target discrete measure in this frame. Furthermore, we derive quantitative bounds ...

A Gradient Weighted Moving Finite-Element Method with Polynomial Approximation of Any Degree

Stability of Solutions to Generalized Forchheimer Equations of Any Degree

ABSTRACT. The non-linear Forchheimer equations are considered as laws of hydrodynamics in porous media in case of high Reynolds numbers, when the fluid flows deviate from the ubiquitous Darcy’s law. In this article, the dynamics of generalized Forchheimer equations for slightly compressible fluids are studied by means of the resulting initial boundary value problem for the pressure. We prove th...

Degree of Adaptive Approximation

We obtain various estimates for the error in adaptive approximation and also establish a relationship between adaptive approximation and free-knot spline approximation.