The block-Toeplitz-matrix based CG-FFT algorithm with an inexact sparse preconditioner for analysis of microstrip circuits

2002 ◽  
Vol 34 (5) ◽  
pp. 347-351 ◽  
Author(s):  
R. S. Chen ◽  
Edward K. N. Yung ◽  
K. F. Tsang ◽  
L. Mo
Keyword(s):  
Toeplitz Matrix ◽  
Block Toeplitz Matrix

Block Toeplitz Matrix Inversion

1973 ◽  
Vol 24 (2) ◽  
pp. 234-241 ◽  
Author(s):  
Hirotugu Akaike
Keyword(s):  
Toeplitz Matrix ◽  
Matrix Inversion ◽  
Block Toeplitz Matrix

A fast reduced-rank interpolation method for prestack seismic volumes that depend on four spatial dimensions

Geophysics ◽  
2013 ◽  
Vol 78 (1) ◽  
pp. V21-V30 ◽  
Author(s):  
Jianjun Gao ◽  
Mauricio D. Sacchi ◽  
Xiaohong Chen
Keyword(s):  
Spatial Data ◽  
Toeplitz Matrix ◽  
Seismic Data ◽  
Random Noise ◽  
Computational Cost ◽  
Reconstruction Method ◽  
Rank Reduction ◽  
Lanczos Bidiagonalization ◽  
Reduced Rank ◽  
Block Toeplitz Matrix

Rank reduction strategies can be employed to attenuate noise and for prestack seismic data regularization. We present a fast version of Cadzow reduced-rank reconstruction method. Cadzow reconstruction is implemented by embedding 4D spatial data into a level-four block Toeplitz matrix. Rank reduction of this matrix via the Lanczos bidiagonalization algorithm is used to recover missing observations and to attenuate random noise. The computational cost of the Lanczos bidiagonalization is dominated by the cost of multiplying a level-four block Toeplitz matrix by a vector. This is efficiently implemented via the 4D fast Fourier transform. The proposed algorithm significantly decreases the computational cost of rank-reduction methods for multidimensional seismic data denoising and reconstruction. Synthetic and field prestack data examples are used to examine the effectiveness of the proposed method.

scholarly journals A HYPONORMAL TOEPLITZ COMPLETION PROBLEM

2013 ◽  
Vol 56 (1) ◽  
pp. 1-8
Author(s):  
IN SUNG HWANG ◽  
AN HYUN KIM
Keyword(s):  
Rational Function ◽  
Toeplitz Matrix ◽  
Completion Problem ◽  
Block Toeplitz Matrix ◽  
Formula Group ◽  
Image Position

AbstractIn this paper we consider the following ‘Toeplitz completion’ problem: Complete the unspecified analytic Toeplitz entries of the partial block Toeplitz matrix $ \begin{linenomath} A:=\begin{bmatrix} T_{\overline\psi_1}& ?\\[4pt] \T_{\overline\psi_2} \end{bmatrix} \end{linenomath} $ to make A hyponormal, where ψi∈H∞ is a non-constant rational function for i=1,2.

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