Interpolatory pointwise estimates for monotone polynomial approximation
نویسندگان
چکیده
منابع مشابه
Interpolatory Pointwise Estimates for Polynomial Approximation
We discuss whether or not it is possible to have interpolatory pointwise estimates in the approximation of a function f 2 C 0; 1], by polynomials. For the sake of completeness as well as in order to strengthen some existing results, we discuss brieey the situation in unconstrained approximation. Then we deal with positive and monotone constraints where we show exactly when such interpolatory es...
متن کاملPointwise Estimates for Monotone Polynomial Approximation
We prove that if f is increasing on [ 1,1], then for each n = 1, 2 . . . . . there is an increasing algebraic polynomial P. of degree n such that {f(x) P.(x){ < cw2( f, V/I x 2 /n) , where w2 is the second-order modulus of smoothness. These results complement the classical pointwise estimates of the same type for unconstrained polynomial approximation. Using these results, we characterize the m...
متن کاملPointwise estimates for 3-monotone approximation
We prove that for a 3-monotone function F ∈ C[−1, 1], one can achieve the pointwise estimates |F(x) − Ψ(x)| ≤ cω3(F, ρn(x)), x ∈ [−1, 1], where ρn(x) := 1 n2 + √ 1−x2 n and c is an absolute constant, both with Ψ , a 3-monotone quadratic spline on the nth Chebyshev partition, and with Ψ , a 3-monotone polynomial of degree ≤ n. The basis for the construction of these splines and polynomials is th...
متن کاملPointwise estimates for polynomial approximation on the semiaxis
We state some pointwise estimates for the rate of weighted approximation of a continuous function on the semiaxis by polynomials. Similarly to a previous result in C[−1, 1] due to Z. Ditzian and D. Jiang [2], we consider weighted φ moduli of continuity, where 0 ≤ λ ≤ 1. The results we obtain bridge the gap between an old pointwise estimate by V.M. Fedorov [4] and the recent norm estimates.
متن کاملPointwise a posteriori error estimates for monotone semi-linear equations
We derive upper and lower a posteriori estimates for the maximum norm error in finite element solutions of monotone semi-linear equations. The estimates hold for Lagrange elements of any fixed order, non-smooth nonlinearities, and take numerical integration into account. The proof hinges on constructing continuous barrier functions by correcting the discrete solution appropriately, and then app...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2018
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2017.11.038