Abstract We study the solution set to multivariate Chebyshev approximation problem, focussing on ill-posed case when uniqueness of solutions can not be established via strict polynomial separation. obtain an upper bound dimension and show that nonuniqueness is generic for problems discrete domains. Moreover, given a prescribed points minimal maximal deviation we construct function which best ap...

Let F be a holomorphic map whose components satisfy some polynomial relations. We present an algorithm for constructing Nash maps locally approximating , the same

In this paper, modified solutions were compared through utilizing three different approximate methods for bar structures. The modifications considered various changes in the initial design. To authors' best of knowledge, the studies have carried out on this matter so far are not broad enough and have considerred the simeltaneous variations of size, geometry and topology on the bar structures. I...

The construction of fractional type of flatlet biorthogonal multiwavelet system is investigated in this paper. We apply this system as basis functions to solve the fractional differential and integro-differential equations. Biorthogonality and high vanishing moments of this system are two major properties which lead to the good approximation for the solutions of the given problems. Some test pr...

Recently, numerical solutions of stochastic differential equations have received a great deal of attention. Numerical approximation schemes are invaluable tools for exploring its properties. In this paper, we introduce a class of stochastic age-dependent (vintage) capital system with Poisson jumps, and investigate the convergence of numerical approximation. It is proved that the the numerical a...

In practice, evolutionary algorithms are often used to find good feasible solutions to complex optimisation problems in a reasonable running time, rather than the optimal solutions. In theory, an important question we should answer is that: how good approximation solutions can evolutionary algorithms produce in a polynomial time? This paper makes an initial discussion on this question and conne...

In this paper we shall study a fractional integral equation in an arbitrary Banach space X . We used the analytic semigroups theory of linear operators and the fixed point method to establish the existence and uniqueness of solutions of the given problem.We also prove the existence of global solution. The existence and convergence of the Faedo–Galerkin solution to the given problem is also prov...