โ Scribed by Jun Murakami; Naoki Yamamoto; Yoshiaki Tadokoro
No coin nor oath required. For personal study only.
As a method to expand the 3D array by the 3D tensor products, the 3D outer product expansion is proposed and is used in the compression of image data and the design of 3D digital filters. The computational procedure is to apply nonlinear optimization iteratively to derive the expansion coefficients and the expansion vectors. Generally, the problems in nonlinear optimization have been that the process may not converge or a solution other than the optimal may be derived, depending on the given initial value, or the computational complexity and the computation time become tremendous when the size of the 3D array is enlarged. In order to handle these problems, the authors devised a method of calculating the 3D outer product expansion without applying nonlinear optimization, by using the power method, which is known as a numerical eigenvalue computation method. The validity of the method is verified against the calculation results. The computation time can be decreased by applying the proposed method. The calculation also reveals that the orthogonality among the expansion terms is lost in the calculation of the outer product expansion. Consequently, an expansion based on the mathematical definition of the 3D tensor product expansion that satisfies orthogonality is considered, and it is verified that the calculation can be performed in this expansion by 3D outer product expansion by the power method. ยฉ 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 85(7): 63โ72, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.1108
๐ SIMILAR VOLUMES
## Abstract The analysis of structures with complex geometries leads to the use of threeโdimensional numerical methods. Such devices can be unmanageable unless a segmentation technique is applied. In this work, a hybrid 3D finiteโelementโmode matching method, based on the generalized admittance mat