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Journal ArticleDOI
01 Jun 1978
163 Citations
This leads to a unified, compact, and singularity-free approach to determining the quaternion when the matrix is given.
Thus, the first challenge is efficiently updating the PSVD when the matrix is altered slightly.
Here, we propose a rank-one approximation for each blurring kernel image formed by a row vector of the sinogram blurring matrix to improve the stability of the 4-D blurring matrix estimation.
We prove that for matrices of order 4, our construction gives the matrix with the lowest possible fixed XOR cost.
On the other hand, Matrix Factorization algorithms have been shown to perform well for recommender systems, specially when the data is sparse.
In particular, the IKKT matrix model is capable of describing 4-dimensional NC space-times with a general effective metric.
We generate forecasting equations, which can successfully predict movie box office and online DVD store sales.
Journal ArticleDOI
Thomas F. Coleman, Wei Xu 
12 Citations
This auxiliary matrix can be sparse even when the true Jacobian matrix is dense; consequently, sparse matrix technology can be used, to great speed advantage, both in forming the auxiliary matrix and in solving the auxiliary linear system.
Furthermore, it is possible to predict an optional release process when the amount of matrix and composition of matrix system were defined.
We also prove that any complex split quaternion has a 4 × 4 complex matrix representation.
This generalizes previous results for 4-dimensional matrix models.
We show that Yeh’s version is a more accurate approximation to the full 4×4 matrix.
The results show that the newly estimated 4-D blurring matrix can improve the image quality over those obtained with a 2-D blurring matrix and requires less point source scans to achieve similar image quality compared with an unconstrained 4-D blurring matrix estimation.
These results demonstrate that human conjunctival fibroblasts express receptors for IL-4, and that IL-4 stimulates both the proliferation of and the production of extracellular matrix proteins by these cells.

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