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On properties of matrix I(-1) of Sinc methods

Authors: 
Iyad T. Abu-Jeib and Thomas Shores
Journal Name: 
New Zealand J. Math.
Volume: 
32
Issue: 
1
Pages From: 
1
To: 
10
Date: 
Wednesday, January 1, 2003
Keywords: 
Sinc, eigenvalue, eigenvector, singular value, determinant, skew{ symmetric, Toeplitz.
Abstract: 
In this paper, we study the determinant and eigen properties of $I^{(-1)},$ an important Toeplitz matrix used in Sinc methods. Some Sinc method applications depend on the non-singularity of this matrix and on the location of its eigenvalues. Among the theorems we prove is that $I^{(-1)}$ is nonsingular. We also show that if $\lambda $ is a pure imaginary eigenvalue of $I^{(-1)}$, then $|\lambda| > \frac{1}{\pi }$.
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