摘要: Abstract The purpose of this note is to describe some properties a particular positive definite Toeplitz matrix arbitrary order, which we call the prolate matrix. This arises naturally in signal processing, and it extremely ill conditioned. Moreover, its eigenvalues exhibit rather unusual behavior, making very useful test for computational algorithms.
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sci-hub.se 参考文章(10)
F. Alberto Grünbaum, Toeplitz matrices commuting with tridiagonal matrices Linear Algebra and its Applications. ,vol. 40, pp. 25- 36 ,(1981) , 10.1016/0024-3795(81)90138-5
Evgenij E. Tyrtyshnikov, Optimal and superoptimal circulant preconditioners SIAM Journal on Matrix Analysis and Applications. ,vol. 13, pp. 459- 473 ,(1992) , 10.1137/0613030
George Cybenko, The Numerical Stability of the Levinson-Durbin Algorithm for Toeplitz Systems of Equations SIAM Journal on Scientific and Statistical Computing. ,vol. 1, pp. 303- 319 ,(1980) , 10.1137/0901021
Tony F. Chan, An Optimal Circulant Preconditioner for Toeplitz Systems SIAM Journal on Scientific and Statistical Computing. ,vol. 9, pp. 766- 771 ,(1988) , 10.1137/0909051
A. Wyner, An analog scrambling scheme which does not expand bandwidth, Part I: Discrete time IEEE Transactions on Information Theory. ,vol. 25, pp. 261- 274 ,(1979) , 10.1109/TIT.1979.1056050
Feliks Ruvimovich Gantmakher, None, The Theory of Matrices ,(1984)
Raymond H. Chan, Gilbert Strang, Toeplitz Equations by Conjugate Gradients with Circulant Preconditioner SIAM Journal on Scientific and Statistical Computing. ,vol. 10, pp. 104- 119 ,(1989) , 10.1137/0910009
D. Slepian, Prolate spheroidal wave functions, fourier analysis, and uncertainty — V: the discrete case Bell System Technical Journal. ,vol. 57, pp. 1371- 1430 ,(1978) , 10.1002/J.1538-7305.1978.TB02104.X
Leonard J. Savage, Ulf Grenander, Gabor Szego, Toeplitz Forms and Their Applications. Journal of the American Statistical Association. ,vol. 53, pp. 763- ,(1958) , 10.2307/2282065
Gene H Golub, Charles F Van Loan, Matrix computations ,(1983)