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View article: Approximation of the Hilbert Transform On The Unit Circle
Approximation of the Hilbert Transform On The Unit Circle Open
The paper deals with the numerical approximation of the Hilbert transform on the unit circle using Szegő and anti-Szegő quadrature formulas. These schemes exhibit maximum precision with oppositely signed errors and allow for improved accur…
View article: Geometric means of HPD GLT matrix-sequences: a maximal result beyond invertibility assumptions on the GLT symbols
Geometric means of HPD GLT matrix-sequences: a maximal result beyond invertibility assumptions on the GLT symbols Open
In the current work, we consider the study of the spectral distribution of the geometric mean matrix-sequence of two matrix-sequences $\{G(A_n, B_n)\}_n$ formed by Hermitian Positive Definite (HPD) matrices, assuming that the two input mat…
View article: Blocking structures, approximation, and preconditioning
Blocking structures, approximation, and preconditioning Open
We consider block-structured matrices $A_n$, where the blocks are of (block) unilevel Toeplitz type with $s\times t$ matrix-valued generating functions. Under mild assumptions on the size of the (rectangular) blocks, the asymptotic distrib…
View article: Approximation of the Hilbert Transform on the unit circle
Approximation of the Hilbert Transform on the unit circle Open
The paper deals with the numerical approximation of the Hilbert transform on the unit circle using Szegö and anti-Szegö quadrature formulas. These schemes exhibit maximum precision with oppositely signed errors and allow for improved accur…
View article: A note on eigenvalues and singular values of variable Toeplitz matrices and matrix-sequences, with application to variable two-step BDF approximations to parabolic equations
A note on eigenvalues and singular values of variable Toeplitz matrices and matrix-sequences, with application to variable two-step BDF approximations to parabolic equations Open
Here, we consider a more general class of matrix-sequences and we prove that they belong to the maximal $*$-algebra of generalized locally Toeplitz (GLT) matrix-sequences. Then, we identify the associated GLT symbols and GLT momentary symb…