scholarly journals Construction algorithms for higher order polynomial lattice rules

2011 ◽  
Vol 27 (3-4) ◽  
pp. 281-299 ◽  
Author(s):  
Jan Baldeaux ◽  
Josef Dick ◽  
Julia Greslehner ◽  
Friedrich Pillichshammer
Keyword(s):  
Higher Order ◽  
Lattice Rules ◽  
Order Polynomial ◽  
Construction Algorithms

scholarly journals Efficient calculation of the worst-case error and (fast) component-by-component construction of higher order polynomial lattice rules

2011 ◽  
Vol 59 (3) ◽  
pp. 403-431 ◽  
Author(s):  
Jan Baldeaux ◽  
Josef Dick ◽  
Gunther Leobacher ◽  
Dirk Nuyens ◽  
Friedrich Pillichshammer
Keyword(s):  
Higher Order ◽  
Fast Component ◽  
Lattice Rules ◽  
Worst Case ◽  
Efficient Calculation ◽  
Order Polynomial

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

scholarly journals Construction algorithms for polynomial lattice rules for multivariate integration

2005 ◽  
Vol 74 (252) ◽  
pp. 1895-1922 ◽  
Author(s):  
J. Dick ◽  
F. Y. Kuo ◽  
F. Pillichshammer ◽  
I. H. Sloan
Keyword(s):  
Lattice Rules ◽  
Multivariate Integration ◽  
Construction Algorithms

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.

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