The following is a special case of the problem to be considered in this paper : Given a function cb(x) of the real variable x, continuous on a finite interval (a, b) ; to determine the polynomial p(x) of given degree n, which gives the closest approximation to the given function cp on the interval (a, b). This problem becomes definite only when the meaning of the phrase " closest approximation ...

where x(t) ∈ D ⊂ Rp and f (x) ∈ R is an unknown function but assumed to be bounded function in x. When the structure of the uncertainty is unknown, function approximation is usually employed to estimate the unknown function. In recent years, neural networks have gained a lot of attention in function approximation theory in connection with adaptive control. Multi-layer neural networks have the c...

the gravity recovery and climate experiment (grace), twin satellites launched in march 2002, are making detailed measurements of the earth's gravity field. it will yield discoveries about gravity and the earth's natural systems. different sensors and instruments have been placed in the grace satellites to fulfill the primary scientific objective of the mission in mapping the earth’s g...

In this paper we generalize and extend BrosowskiMeinardus type results on invariant points from the set of best approximation to the set of best simultaneous approximation, which is not necessarily starshaped. As a consequence some results on best approximation are deduced. The proved results extend and generalize some of the results of R. N. Mukherjee and V. Verma [Publ. de l’Inst. Math. 49(19...

we show that the character space of the vector-valued lipschitz algebra $lip^{alpha}(x, e)$ of order $alpha$ is homeomorphic to the cartesian product $xtimes m_e$ in the product topology, where $x$ is a compact metric space and $e$ is a unital commutative banach algebra. we also characterize the form of each character on $lip^{alpha}(x, e)$. by appealing to the injective tensor product, we then...

We are concerned with the problem of scheduling monotonic moldable tasks on identical processors to minimize makespan. focus natural case where number m as resources is fixed or relatively small compared n tasks. present an efficient (3/2)-approximation algorithm time complexity O(nmlog(nm)) (for m>n) and O(n2logn) m?n). To best our knowledge, relevant known results are: (a) a (3/2+?)-approxima...

We present a polynomial-time 9/7-approximation algorithm for the graphic TSP for cubic graphs, which improves the previously best approximation factor of 1.3 for 2-connected cubic graphs and drops the requirement of 2-connectivity at the same time. To design our algorithm, we prove that every simple 2-connected cubic n-vertex graph contains a spanning closed walk of length at most 9n/7− 1, and ...

The paper deals with the Lagrange interpolation of functions having a bounded variation derivative. For special systems of nodes, it is shown that this polynomial sequence converges with the best approximation order. The L weighted case is also discussed.