Higher-order polynomial approximation

2016 ◽  
Vol 8 (2) ◽  
pp. 183-200 ◽  
Author(s):  
N. D. Dikusar
Keyword(s):  
Polynomial Approximation ◽  
Higher Order ◽  
Order Polynomial

scholarly journals Pointwise estimates for higher order convexity preserving polynomial approximation

1994 ◽  
Vol 36 (2) ◽  
pp. 213-233 ◽  
Author(s):  
Jia-Ding Cao ◽  
Heinz H. Gonska
Keyword(s):  
Polynomial Approximation ◽  
Convex Functions ◽  
Higher Order ◽  
Second Order ◽  
Convolution Type ◽  
Shape Preservation ◽  
Moduli Of Continuity ◽  
Pointwise Estimates ◽  
Higher Order Convexity ◽  
Boolean Sum

AbstractDeVore-Gopengauz-type operators have attracted some interest over the recent years. Here we investigate their relationship to shape preservation. We construct certain positive convolution-type operators Hn, s, j which leave the cones of j-convex functions invariant and give Timan-type inequalities for these. We also consider Boolean sum modifications of the operators Hn, s, j show that they basically have the same shape preservation behavior while interpolating at the endpoints of [−1, 1], and also satisfy Telyakovskiῐ- and DeVore-Gopengauz-type inequalities involving the first and second order moduli of continuity, respectively. Our results thus generalize related results by Lorentz and Zeller, Shvedov, Beatson, DeVore, Yu and Leviatan.

scholarly journals On the existence of higher order polynomial lattices based on a generalized figure of merit

2007 ◽  
Vol 23 (4-6) ◽  
pp. 581-593 ◽  
Author(s):  
Josef Dick ◽  
Peter Kritzer ◽  
Friedrich Pillichshammer ◽  
Wolfgang Ch. Schmid
Keyword(s):  
Figure Of Merit ◽  
Higher Order ◽  
Order Polynomial

Polynomial Definiteness and Semidefiniteness

1970 ◽  
Vol 92 (2) ◽  
pp. 394-397 ◽  
Author(s):  
Chiou-Shiun Chen ◽  
Edwin Kinnen
Keyword(s):  
Quadratic Form ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Real Polynomial ◽  
Reduction Procedure ◽  
Sign Definiteness ◽  
Order Polynomial ◽  
The Individual ◽  
New Variables ◽  
Engineering Stability

A reduction procedure is described for determining the sign definiteness and semidefiniteness of an mth order, n dimensional real polynomial. The higher order polynomial is reduced to a quadratic form in new variables such that conditions can be obtained on the coefficients of the individual terms of the original polynomial. The procedure presents sufficient conditions only. It has been found, however, to be a relatively systematic technique for engineering stability problems where alternate effective methods for determining sign definiteness are unknown.

EXTRACTING LYAPUNOV EXPONENTS FROM SHORT TIME SERIES OF LOW PRECISION

1992 ◽  
Vol 06 (02) ◽  
pp. 55-75 ◽  
Author(s):  
X. ZENG ◽  
R.A. PIELKE ◽  
R. EYKHOLT
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Polynomial Approximation ◽  
Qr Decomposition ◽  
Short Time Series ◽  
Order Polynomial ◽  
Free Parameters ◽  
Short Time ◽  
Lyapunov Exponent Spectrum

Different methods for computing the Lyapunov-exponent spectrum from a time series are reviewed. All algorithms are based on either Gram-Schmidt orthonormalization or Householder QR decomposition, and they use either the linearized map or a higher-order polynomial approximation. They also differ in implementation details. The ability to use these methods for a short time series of low precision is investigated, with special attention being given to the practicality of these algorithms; i.e., their efficiency and accuracy and the number of adjustable free parameters.

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