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Eigenvalues and Eigenvectors
Published in Sohail A. Dianat, Eli S. Saber, ®, 2017
Sohail A. Dianat, Eli S. Saber
One of the most important tools in signal processing and numerical linear algebra is the singular value decomposition (SVD) of matrices. SVD was developed for square matrices by Beltrami and Jordan in the 18th century. The theory for general matrices was established by Eckart and Young. We first state the SVD theorem and then explore its use in several engineering applications.
Numerical and Computational Issues in Linear Control and System Theory
Published in William S. Levine, Control System Fundamentals, 2019
A.J. Laub, R.V. Patel, P.M. Van Dooren
One of the basic and most important tools of modern numerical analysis, especially numerical linear algebra, is the singular value decomposition (SVD). Here we make a few comments about its properties and computation as well as its significance in various numerical problems.
A study and implementation of large-scale log-determinant computation to cloud
Published in International Journal of Computers and Applications, 2021
Md. Alamgir Hossain, Jannatul Ferdush, Marjia Khatun
Devices from numerical linear algebra, for example, determinant, matrix inversion linear solvers, eigenvalue calculation, and other matrix disintegrations, have been playing an essential hypothetical and computational job for AI applications. While most network calculations concede polynomial-time calculations, they are frequently infeasible for extensive scale or high-dimensional informational indexes. In this paper, we structure and investigate a high exactness straight time estimate calculation for the logarithm of matrix determinants, where its precise calculation requires cubic-time. Besides, it is anything but difficult to parallelize since it requires just (detachable) lattice vector duplications. We trust that the proposed convention will discover various applications in AI issues. In this paper, we have planned a condition of-the-practice convention for outsourcing to a malignant cloud. It is demonstrated that the proposed convention all the while satisfies the objectives of rightness, security (input/output protection), certainty and high-effectiveness. With the appearance of expansive scale information and distributed computing period, there is an expanding requirement for a very much incorporated logical calculations redistributing programing framework, which ought to almost certainly give secure outsourcing administrations to a wide range of ordinarily utilized logical calculations. We imagine that such an incorporated programing framework possesses interface in the customer side like Matlab, though it moves the substantial calculation to the cloud server. We have planned a condition of the training convention for the outsourcing of LDC in this paper, a stage forward to construct such an incorporated programing framework. At last, we can say that this proposition paper depicts about from begin to finish about extensive framework Log-determinant calculation in an open pernicious cloud.