Results 61 to 70 of about 186,989 (178)

Modified Bernstein Polynomials and Jacobi Polynomials in q-Calculus

, 2004
We introduce here a generalization of the modified Bernstein polynomials for Jacobi weights using the $q$-Bernstein basis proposed by G.M. Phillips to generalize classical Bernstein Polynomials.
Derriennic, Marie-Madeleine
core   +3 more sources

On the Complexity of Optimization over the Standard Simplex [PDF]

We review complexity results for minimizing polynomials over the standard simplex and unit hypercube.In addition, we show that there exists a polynomial time approximation scheme (PTAS) for minimizing Lipschitz continuous functions and functions with ...
Elfadul, G.E.E., Hertog, D. den, Klerk, E. de   +2 more
core   +1 more source

Combinatorial identities associated with new families of the numbers and polynomials and their approximation values

, 2017
Recently, the numbers $Y_{n}(\lambda )$ and the polynomials $Y_{n}(x,\lambda)$ have been introduced by the second author [22]. The purpose of this paper is to construct higher-order of these numbers and polynomials with their generating functions.
Kucukoglu, Irem, Simsek, Yilmaz
core  

Approximation by q-Bernstein Polynomials in the Case q→1+

Abstract and Applied Analysis, 2014
Let Bn,q(f;x), q∈(0,∞) be the q-Bernstein polynomials of a function f∈C[0,1]. It has been known that, in general, the sequence Bn,qn(f) with qn→1+ is not an approximating sequence for f∈C[0,1], in contrast to the standard case qn→1-.
Xuezhi Wu
doaj   +1 more source

Approximation by Polynomials with Restricted Zeros

Journal of Approximation Theory, 1994
The authors have discussed convergence properties of polynomials \(p(z)\) whose zeros lie on the real axis or in the upper half-plane \((\text{Im } z\geq 0)\). A result of \textit{B. Ya. Levin} [Mat. Sb., N. Ser. 66(108), 384-397 (1965; Zbl 0145.303)] shows that uniform convergence of such polynomials to a non-zero limit on a complex sequence ...
Clunie, J.G., Kuijlaars, A.B.J.
openaire   +4 more sources

Exponential Splines and Pseudo-Splines: Generation versus reproduction of exponential polynomials

, 2014
Subdivision schemes are iterative methods for the design of smooth curves and surfaces. Any linear subdivision scheme can be identified by a sequence of Laurent polynomials, also called subdivision symbols, which describe the linear rules determining ...
Conti, Costanza, Gemignani, Luca, Romani, Lucia   +2 more
core  

Optimal Piecewise Polynomial Approximation for Minimum Computing Cost by Using Constrained Least Squares

Sensors
In this paper, the optimal approximation algorithm is proposed to simplify non-linear functions and/or discrete data as piecewise polynomials by using the constrained least squares.
Jieun Song, Bumjoo Lee
doaj   +1 more source

Approximation by weighted polynomials

Journal of Approximation Theory, 2003
The paper is devoted to the study of approximation by weighted polynomials. The author proves that if \(xQ'(x)\) is increasing on \((0,\infty)\) and \(w(x)= \exp(-Q(x))\) is the corresponding weight on \([0,\infty)\), then every continuous function that vanishes outside.
openaire   +1 more source

Explicitly solvable complex Chebyshev approximation problems related to sine polynomials [PDF]

Explicitly solvable real Chebyshev approximation problems on the unit interval are typically characterized by simple error curves. A similar principle is presented for complex approximation problems with error curves induced by sine polynomials.
Freund, Roland
core   +1 more source

Mean Convergence Rate of Derivatives by Lagrange Interpolation on Chebyshev Grids

Discrete Dynamics in Nature and Society, 2011
We consider the rate of mean convergence of derivatives by Lagrange interpolation operators based on the Chebyshev nodes. Some estimates of error of the derivatives approximation in terms of the error of best approximation by polynomials are derived. Our
Wang Xiulian, Ning Jingrui
doaj   +1 more source