On uniform approximation to real numbers

On approximation of real numbers by real algebraic numbers

A uniform approximation method to solve absolute value equation

In this paper, we propose a parametric uniform approximation method to solve NP-hard absolute value equations. For this, we uniformly approximate absolute value in such a way that the nonsmooth absolute value equation can be formulated as a smooth nonlinear equation. By solving the parametric smooth nonlinear equation using Newton method, for a decreasing sequence of parameters, we can get the ...

Approximation to Real Numbers by Cubic Algebraic Integers I

The study of approximation to a real number by algebraic numbers of bounded degree started with a paper of E. Wirsing [10] in 1961. Motivated by this, H. Davenport and W. M. Schmidt considered in [5] the analogous inhomogeneous problem of approximation to a real number by algebraic integers of bounded degree. They proved a result that is optimal for degree 2 and a general result which is valid ...

Approximation to real numbers by cubic algebraic integers . II

It has been conjectured for some time that, for any integer n ≥ 2, any real number ε > 0 and any transcendental real number ξ, there would exist infinitely many algebraic integers α of degree at most n with the property that |ξ−α| ≤ H(α)−n+ε, where H(α) denotes the height of α. Although this is true for n = 2, we show here that, for n = 3, the optimal exponent of approximation is not 3 but (3 +...

On Constrained Uniform Approximation