U. Grenander and G. Szego, Toeplitz Forms and Their Applications, 2nd Ed., Chelsea Publishing Co., New York, 1981. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
The Parallel-Gaussian Watermarking Game - Moulin, Mihçak (2002) (5 citations) (Correct)
....equivalent [17, 18] i.e. they are uniformly bounded (by 1 #) in strong norm, and lim N## R N RK,N HS = 0, where A HS = T r(A T A) 1 2 denotes the Hilbert Schmidt (weak) norm of a matrix. The relative entropy between the Gaussian distributions P N and P N K is given by [16, 17] D(P N P N K ) 1 2 ln det RK,N R 1 N 1 2 1 2 T r(RK,N R 1 N ) 1 2 ln det RK,N 1 2 ln det RN 1 2 1 2 T r(RK,N R 1 N ) where 1 N ln det RK,N = 1 K ln det RK O(1 N) 1 N ln det RN # ## ln #(f) df, T r(RK,N R 1 N ) # T r(RK,N TN ) as N ##. Now # l # ....
....Parseval s identity, we obtain 1 N T r(RK,N R 1 N ) # # n#Z (wK,n r n )t n = ## # K (f) #(f) df and so lim N## 1 N D(P N P N K ) 1 2 # ## ln #(f) df 1 K ln det RK # 1 2 1 2 ## # K (f) #(f) df. E. 1) Now lim K## 1 K ln det RK = ## ln #(f) df [16]. Also lim K## ## # K (f) #(f) df = 1, because # K converges uniformly to # over# (by continuity of #) and #(f) is bounded away from zero. Hence (6.1) follows. # F Proof of Theorem 6.2 Given two K dimensional vectors r = r k K k=1 and s = s k K k=1 , let C (K) r, s) max ....
[Article contains additional citation context not shown here]
U. Grenander and G. Szego, Toeplitz Forms and Their Applications, 2nd Ed., Chelsea Publishing Co., New York, 1981.
The Parallel-Gaussian Watermarking Game - Pierre Moulin And (2000) (5 citations) (Correct)
No context found.
U. Grenander and G. Szego, Toeplitz Forms and Their Applications, 2nd Ed., Chelsea Publishing Co., New York, 1981.
Spectral Measure Of Large Random Hankel, - Markov And Toeplitz (Correct)
No context found.
Ulf Grenander and Gabor Szeg}o. Toeplitz forms and their applications. Chelsea Publishing Co., New York, second edition, 1984.
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC