Accelerating the Distributed Kaczmarz Algorithm by Strong Over-relaxation
| Autor: | Steven N. Harding, Chloe Makdad, Randal Tuggle, Eric Weber, Riley Borgard, Haley Duba, Jay Mayfield |
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| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Numerical Analysis
Algebra and Number Theory 010102 general mathematics 010103 numerical & computational mathematics Numerical Analysis (math.NA) Network topology 01 natural sciences 15A06 15A24 Kaczmarz algorithm Optimization and Control (math.OC) Norm (mathematics) FOS: Mathematics Discrete Mathematics and Combinatorics Geometry and Topology Mathematics - Numerical Analysis 0101 mathematics Algorithm Mathematics - Optimization and Control Mathematics |
| Popis: | The distributed Kaczmarz algorithm is an adaptation of the standard Kaczmarz algorithm to the situation in which data is distributed throughout a network represented by a tree. We isolate substructures of the network and study convergence of the distributed Kaczmarz algorithm for relatively large relaxation parameters associated to these substructures. If the system is consistent, then the algorithm converges to the solution of minimal norm; however, if the system is inconsistent, then the algorithm converges to an approximated least-squares solution that is dependent on the parameters and the network topology. We show that the relaxation parameters may be larger than the standard upper-bound in literature in this context and provide numerical experiments to support our results. |
| Databáze: | OpenAIRE |
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