We discuss a generalization of the Cohn–Umans method, a potent technique developed for studying the bilinear complexity of matrix multiplication by embedding matrices into an appropriate group algebra. We investigate how the Cohn–Umans method may be used for bilinear operations other than matrix multiplication, with algebras other than group algebras, and we relate it to Strassen’s tensor rank ...

A set of new formulae for the inverse of a block Hankel (or block Toeplitz) matrix is given. The formulae are expressed in terms of certain matrix Pad6 forms, which approximate a matrix power series associated with the block Hankel matrix. By using Frobenius-type identities between certain matrix Pad6 forms, the inversion formulae are shown to generalize the formulae of Gohberg-Heinig and, in t...

Blur removal is an important problem in signal and image processing. The blurring matrices obtained by using the zero boundary condition (corresponding to assuming dark background outside the scene) are Toeplitz matrices for one-dimensional problems and block-Toeplitz–Toeplitzblock matrices for two-dimensional cases. They are computationally intensive to invert especially in the block case. If ...

In this papers, we investigate the Hankel determinant and Toeplitz for class Bazileviˇc Function B1(α, δ) related to Bernoulli Lemniscate function on unit disk D = {z : |z| < 1} obtain upper bounds of H2(1), H2(2), T2(1), H2(1) using coefficients invers function. We used lemma from Charateodory-Toeplitz Libera about sharp inequalities functions with positive real part.

Matrices with the structures of Toeplitz, Hankel, Vandermonde and Cauchy types are omnipresent in modern computations in Sciences, Engineering and Signal and Image Processing. The four matrix classes have distinct features, but in [P90] we showed that Vandermonde and Hankel multipliers transform all these structures into each other and proposed to employ this property in order to extend any suc...

We show that an infinite Toeplitz+Hankel matrix $T(\varphi ) + H(\psi )$ generates a bounded [compact] operator on $\ell ^p(\mathbb N _0)$ with $1\leq p\leq \infty $ if and only both $H(\psi are [compact]. also give anal