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Bounds for the Z-eigenpair of general nonnegative tensors

100%
Liu Q., Li Y.
Open Mathematics
|
2016
|
tom 14
|
nr 1
181-194
EN
In this paper, we consider the Z-eigenpair of a tensor. A lower bound and an upper bound for the Z-spectral radius of a weakly symmetric nonnegative irreducible tensor are presented. Furthermore, upper bounds of Z-spectral radius of nonnegative tensors and general tensors are given. The proposed bounds improve some existing ones. Numerical examples are reported to show the effectiveness of the proposed bounds.
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An Extension of 3D Zernike Moments for Shape Description and Retrieval of Maps Defined in Rectangular Solids

100%
Sit A., Mitchell J. C., Phillips G. N., Wright S. J.
Molecular Based Mathematical Biology
|
2013
|
tom 1
75-89
EN
Zernike polynomials have been widely used in the description and shape retrieval of 3D objects. These orthonormal polynomials allow for efficient description and reconstruction of objects that can be scaled to fit within the unit ball. However, maps defined within box-shaped regions ¶ for example, rectangular prisms or cubes ¶ are not well suited to representation by Zernike polynomials, because these functions are not orthogonal over such regions. In particular, the representations require many expansion terms to describe object features along the edges and corners of the region. We overcome this problem by applying a Gram-Schmidt process to re-orthogonalize the Zernike polynomials so that they recover the orthonormality property over a specified box-shaped domain. We compare the shape retrieval performance of these new polynomial bases to that of the classical Zernike unit-ball polynomials.
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