Computationally Efficient Reduced Polynomial Based Algorithms for Hermitian Toeplitz Matrices.

摘要

In this work, the mathematical structure is analyzed that is associated with the fast order recursive algorithms for computing the reflection coefficients, and the Levinson polynomial associated with a hermitian, positive definite Toeplitz matrix. A new form of three-term recurrence relation is derived and a computationally efficient alternative to the classical Levinson-Durbin algorithm is obtained. The computational complexity of the new algorithm is the same as those of the split algorithms described in the recent literature. The new algorithm also provides further insight into the mathematical properties of the structurally rich Toeplitz matrices. Keywords: Hermitian Toeplitz matrices; Order recursive algorithms; Levinson polynomial; Reflection coefficients; Reprints. (JHD)