Bowtie factors of Toeplitz matrices by means of split algorithms
C.J. Demeure · IEEE Transactions on Acoustics Speech and Signal Processing · 1989
The bowtie factorization of a Toeplitz correlation matrix R and its inverse is introduced. The term bowtie describes the pattern of the factoring matrices. Several mathematical properties of bowtie matrices are described, including their close relation with block triangular matrices. The bowtie factors of the inverse R can be computed using a vector version of the split Levinson algorithm, restricted to orders with the same parity as n, the dimension of R. The bowtie factors of R can be computed using split vector versions of the Schur algorithm. The orthogonal factorization of the underlying data matrix Y can also be computed by the split versions of the lattice algorithm, producing a bowtie orthogonal factor of Y.>