New algorithms for Toeplitz and Toeplitz-plus-Hankel are presented that are in the spirit of the “split” algorithms of Delsarte/Genin. It is shown that the split algorithms are related to ZW-factorizations like the classical algorithms are related to LU-factorizations. Special attention is paid to skewsymmetric Toeplitz, centrosymmetric Toeplitz-plus-Hankel and general Toeplitz-plus-Hankel matr...

We give a brief survey of subnormality and hyponormality of Toeplitz operators on the vector-valued Hardy space of the unit circle. We also solve the following subnormal Toeplitz completion problem: Complete the unspecified rational Toeplitz operators (i.e., the unknown entries are rational Toeplitz operators) of the partial block Toeplitz matrix

ABSTRACT A Toeplitz-block-Toeplitz (TBT) matrix is block Toeplitz with Toeplitz blocks. TBT systems of equations arise in 2D interpolation, 2-D linear prediction and 2-D least-squares deconvolution problems. Although the doubly Toeplitz structure should be exploitable in a fast algorithm, existing fast algorithms only exploit the block Toeplitz structure, not the Toeplitz structure of the block...

A fast solution algorithm is proposed for solving block banded block Toeplitz systems with non-banded Toeplitz blocks. The algorithm constructs the circulant transformation of a given Toeplitz system and then by means of the Sherman-Morrison-Woodbury formula transforms its inverse to an inverse of the original matrix. The block circulant matrix with Toeplitz blocks is converted to a block diago...

The conjecture of Fisher and Hartwig, published in 1968, describes the asymptotic expansion of Toeplitz determinants with singular generating functions. For more than twenty years progress was made in extending the validity of the conjecture, but recent computer experiments led to counter-examples that show the limits of the original conjecture and pointed the way to a revised conjecture. This ...

We reduce several computations with Hilbert and Vandermonde type matrices to matrix computations of the Hankel-Toeplitz type (and vice versa). This unifies various known algorithms for computations with dense structured matrices and enables us to extend any progress in computations with matrices of one class to the computations with other classes of matrices. In particular, this enables us to c...

we introduce a matricial toeplitz transform and prove that the toeplitz transform of a second order recurrence sequence is another second order recurrence sequence. we investigate the injectivity of this transform and show how this distinguishes the fibonacci sequence among other recurrence sequences. we then obtain new fibonacci identities as an application of our transform.

Hamiltonian Cycles in Directed Toeplitz Graphs Dr Shabnam Malik Faculty of Mathematics, Forman Christian College University, Lahore Pakistan An (n × n) matrix A = (aij) is called a Toeplitz matrix if it has constant values along all diagonals parallel to the main diagonal. A directed Toeplitz graph is a digraph with Toeplitz adjacency matrix. In this talk I will discuss conditions for the exist...

We show that every n × n matrix is generically a product of n/2 + 1 Toeplitz matrices and always a product of at most 2n + 5 Toeplitz matrices. The same result holds true if the word ‘Toeplitz’ is replaced by ‘Hankel,’ and the generic bound n/2 + 1 is sharp. We will see that these decompositions into Toeplitz or Hankel factors are unusual: We may not, in general, replace the subspace of Toeplit...

In this paper, we consider the approximation of dense block Toeplitz-plus-Hankel matrices by sums of Kronecker products. We present an algorithm for efficiently computing the matrix approximation that requires the factorization of matrices of much smaller dimension than that of the original. The main results are described for block Toeplitz matrices with Toeplitz-plus-Hankel blocks (BTTHB), but...