Universal optimality of digital nets and lattice designs

作者：Ai MingYao^*; Hickernell Fred J

来源：Science in China Series A-Mathematics, 2009, 52(11): 2309-2320.

DOI：10.1007/s11425-009-0171-y

• Chebyshev polynomial
• Haar wavelet
• Trigonometric function
• Walsh function

This article considers universal optimality of digital nets and lattice designs in a regression model Based on the equivalence theorem for matrix means and majorization theory, the necessary and sufficient conditions for lattice designs being phi(p)- and universally optimal in trigonometric function and Chebyshev polynomial regression models are obtained. It is shown that digital nets are universally optimal for both complete and incomplete Walsh function regression models under some specified conditions, and are also universally optimal for complete Haar wavelet regression models but may not for incomplete Haar wavelet regression models

• 出版日期2009-11
• 单位北京大学