Spectral properties of banded Toeplitz matrices

2007 ◽  
Vol 39 (2) ◽  
pp. 348-350
Author(s):  
Jonathan R. Partington
Keyword(s):  
Spectral Properties ◽  
Toeplitz Matrices

CONVERGENCE OF A CLASS OF TOEPLITZ TYPE MATRICES

2013 ◽  
Vol 02 (03) ◽  
pp. 1350006
Author(s):  
ARUP BOSE ◽  
SREELA GANGOPADHYAY ◽  
KOUSHIK SAHA
Keyword(s):  
Limit Theorem ◽  
Method Of Moments ◽  
Spectral Properties ◽  
Toeplitz Matrices

We use the method of moments to study the spectral properties in the bulk for finite diagonal large dimensional random and non-random Toeplitz type matrices via the joint convergence of matrices in an appropriate sense. As a consequence we revisit the famous limit theorem of Szegö for non-random symmetric Toeplitz matrices.

An observation on certain spectral properties of Toeplitz matrices

CALCOLO ◽  
1991 ◽  
Vol 28 (1-2) ◽  
pp. 37-43 ◽  
Author(s):  
D. Bini ◽  
F. Di Benedetto
Keyword(s):  
Spectral Properties ◽  
Toeplitz Matrices

scholarly journals BIOLOGICALLY INSPIRED FILTERS UTILIZING SPECTRAL PROPERTIES OF TOEPLITZ-BLOCK-TOEPLITZ MATRICES

2015 ◽  
pp. 198-207
Author(s):  
Dragan Vidacic ◽  
Richard A. Messner
Keyword(s):  
Spectral Properties ◽  
Toeplitz Matrices ◽  
Polar Angle ◽  
Connection Matrix ◽  
Biologically Inspired ◽  
Linear Networks ◽  
Network Connection ◽  
Large Matrix ◽  
Matrix Eigenvalues ◽  
Invariant Coupling

The construction of filters arising from linear neural networks with feed-backward excitatory-inhibitory connections is presented. Spatially invariant coupling between neurons and the distribution of neuron-receptor units in the form of a uniform square grid yield the TBT (Toeplitz-Block-Toeplitz) connection matrix. Utilizing the relationship between spectral properties of such matrices and their generating functions, the method for construction of recurrent linear networks is addressed. By appropriately bounding the generating function, the connection matrix eigenvalues are kept in the desired range allowing for large matrix inverse to be approximated by a convergent power series. Instead of matrix inversion, the single pass convolution with the filter obtained from the network connection weights is applied when solving the network. For the case of inter-neuron coupling in the form of a function that is expandable in a Fourier series in polar angle, the network response filter is shown to be steerable.

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