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Distributed Steepest Descent - A method for distributed linear least squares problems

K. van Geffen, (2016) Distributed Steepest Descent - A method for distributed linear least squares problems. Master's Thesis / Essay, Applied Mathematics.

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Abstract

The need for distributed processing arises naturally in for example wireless sensor networks, smart grids and some filter applications. All the computations are done by autonomous agents, where the communication among agents is restricted by the network topology. In this context, local measurements define, together, a global linear least square problem. Some of the existing methods are characterized by a two-step update of (i) a local minimization and (ii) a communication step. These methods are preferred for the computationally cheap updates, the scalability in network size and the minimal amount of data exchange. In this thesis we focus on two such methods, namely the decentralized gradient descent (DGD) method, which is a gradient descent based method, and the kernel projection (KP) method, which is based on local projection. We establish a link between the two widely different methods and propose two intermediate methods, namely an α- and β-variant of the distributed steepest descent (DSD) method. To this end, we introduce a steepest descent method for underdetermined system (SDud) and establish linear convergence results. When executed until convergence, we show that SDud essentially solves the local projection problem for KP. Additionally, we show that an application of the conjugate gradient method, CGud, computes this projection more efficiently. Finally, we consider numerical experiments and observe that DSD can be competitive with DGD and KP.

Item Type: Thesis (Master's Thesis / Essay)
Degree programme: Applied Mathematics
Thesis type: Master's Thesis / Essay
Language: English
Date Deposited: 15 Feb 2018 08:30
Last Modified: 15 Feb 2018 08:30
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/15545

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