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 Higher-Order SVD (HOSVD) is a generalization of the Singular Value Decomposition (SVD) to higher-order tensors (i.e. arrays with more than two indices) and plays an important role in various domains. Unfortunately, this decomposition is computationally demanding. Indeed, the HOSVD of a third-order tensor involves the computation of the SVD of three matrices, which are referred to as "modes"...

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.

Some properties of near-Toeplitz tridiagonal matrices with specific perturbations in the first and last main diagonal entries are considered. Applying the relation between the determinant and Chebyshev polynomial of the second kind, we first give the explicit expressions of determinant and characteristic polynomial, then eigenvalues are shown by finding the roots of the characteristic polynomia...

This paper proposes a new cumulant-based algorithm to jointly estimate four-dimensional (4D) source parameters of multiple near-field narrowband sources. Firstly, this approach proposes a new cross-array, and constructs five high-dimensional Toeplitz matrices using the fourth-order cumulants of some properly chosen sensor outputs; secondly, it forms a parallel factor (PARAFAC) model in the cumu...

The only non-trivial step in evaluation of the maximum entropy spectral estimate is the computation of the vectorB−1 ·e0. Generic algorithms with run time O(m) can be used for this purpose (e.g. a Cholesky decomposition). However, if run time is critical, the special structure of the Toeplitz matrix should be exploited. Levinson’s algorithm provides a simple and highly efficient way to do this....

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...

An implicit-explicit Euler scheme in temporal direction is employed to discretize a partial integro-differential equation, which arises in pricing options under jumpdiffusion process. Then the semi-discretized equation is approximated in space by the Sinc-Galerkin method with exponential accuracy. Meanwhile, the domain decomposition method is incorporated to handle the non-smoothness of the pay...

The estimation of direction of arrival (DOA) of a smart antenna is not able to perform high resolution in a mixed noise field with high correlation. In this paper, a modified multiple signal classification (MUSIC) algorithm based on spatial difference is proposed for improving the resolution of DoA estimation. The algorithm can eliminate the effect of mixed noise through computing the differenc...

Subspace-based methods have been effectively used to estimate enhanced speech from noisy speech samples. In the traditional subspace approaches, a critical step is splitting of two invariant subspaces associated with signal and noise via subspace decomposition, which is often performed by singular-value decomposition or eigenvalue decomposition. However, these decomposition algorithms are highl...