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      • Department of Computer Engineering
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      Parallel minimum norm solution of sparse block diagonal column overlapped underdetermined systems

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      Author(s)
      Torun, F. S.
      Manguoglu, M.
      Aykanat, Cevdet
      Date
      2017
      Source Title
      ACM Transactions on Mathematical Software
      Print ISSN
      0098-3500
      Publisher
      Association for Computing Machinery
      Volume
      43
      Issue
      4
      Language
      English
      Type
      Article
      Item Usage Stats
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      Abstract
      Underdetermined systems of equations in which the minimum norm solution needs to be computed arise in many applications, such as geophysics, signal processing, and biomedical engineering. In this article, we introduce a new parallel algorithm for obtaining the minimum 2-norm solution of an underdetermined system of equations. The proposed algorithm is based on the Balance scheme, which was originally developed for the parallel solution of banded linear systems. The proposed scheme assumes a generalized banded form where the coefficient matrix has column overlapped block structure in which the blocks could be dense or sparse. In this article, we implement the more general sparse case. The blocks can be handled independently by any existing sequential or parallel QR factorization library. A smaller reduced system is formed and solved before obtaining the minimum norm solution of the original system in parallel. We experimentally compare and confirm the error bound of the proposed method against the QR factorization based techniques by using true single-precision arithmetic. We implement the proposed algorithm by using the message passing paradigm. We demonstrate numerical effectiveness as well as parallel scalability of the proposed algorithm on both shared and distributed memory architectures for solving various types of problems. © 2017 ACM.
      Keywords
      Minimum norm solution
      Parallel algorithms
      Underdetermined least square problems
      Biomedical engineering
      Factorization
      Linear systems
      Memory architecture
      Message passing
      Signal processing
      Balance methods
      Least square problems
      Message passing paradigms
      Numerical effectiveness
      Parallel scalability
      Shared and distributed memory architectures
      Underdetermined systems
      Least squares approximations
      Permalink
      http://hdl.handle.net/11693/37069
      Published Version (Please cite this version)
      http://dx.doi.org/10.1145/3004280
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      • Department of Computer Engineering 1510
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