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An efficient algorithm for the computation of tr{TR/sup -1/}, where T and R are Toeplitz matrices and R is also symmetric positive definite, is presented. The method exploits the fact that the trace of TR/sup -1/ depends only on the sum of the diagonals of R/sup -1/, and not on the whole matrix R/sup -1/. To obtain this sum, a fast efficient technique, built upon the Trench (1964) algorithm for computing the inverse of a Toeplitz matrix, is developed. The complexity of the algorithm depends on the generation function of matrix R and is O(N ln N) for generic functions and O(p ln p) for AR(p) functions.
Published in:
Signal Processing Letters, IEEE
(Volume:9
,
Issue:
2
)
Date of Publication: Feb. 2002
- Page(s):
- 54 - 56
- ISSN :
- 1070-9908
- INSPEC Accession Number:
- 7221184
- Digital Object Identifier :
- 10.1109/97.991137
- Product Type:
- Journals & Magazines
- Date of Current Version :
- 07 August 2002
- Issue Date :
- Feb. 2002
- Sponsored by :
- IEEE Signal Processing Society
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