Randomized Numerical Linear Algebra Approaches for Approximating Matrix Functions
Abstract
This work explores how randomization can be exploited to deliver sophisticated algorithms with provable bounds for: (i) The approximation of matrix functions, such as the log-determinant and the Von-Neumann entropy; and (ii) The low-rank approximation of matrices. Our algorithms are inspired by recent advances in Randomized Numerical Linear Algebra (RandNLA), an interdisciplinary research area that exploits randomization as a computational resource to develop improved algorithms for large-scale linear algebra problems. The main goal of this work is to encourage the practical use of RandNLA approaches to solve Big Data bottlenecks at industrial level. Our extensive evaluation tests are complemented by a thorough theoretical analysis that proves the accuracy of the proposed algorithms and highlights their scalability as the volume of data increases. Finally, the low computational time and memory consumption, combined with simple implementation schemes that can easily be extended in parallel and distributed environments, render our algorithms suitable for use in the development of highly efficient real-world software.
Degree
Ph.D.
Advisors
Drineas, Purdue University.
Subject Area
Mathematics
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