Solving Weighted Least Squares (WLS) problems on ARM-based architectures

Abstract

The Weighted Least Squares algorithm (WLS) is applied to numerous optimization problems, but requires the use of high computational resources, especially when complex arithmetic is involved. This work aims to accelerate the resolution of a WLS problem by reducing the computational cost (relaying on BLAS/LAPACK routines) and the computational precision from double to single. As a test case, we design an IIR filter for a Graphic Equalizer, where the numerical errors due to single precision are easily visualized. In addition, given the importance of low power architectures for this kind of implementations, we evaluate the performance, scalability, and energy efficiency of each method on two different processors implementing the ARMv7 architecture, widely used in current mobile devices with power constraints. Results show that the method that exhibits a high theoretical computational cost overcomes in efficiency other methods with lower theoretical cost in architectures of this type.

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Notes

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    The character(x) in the routine names should be replaced by s, d, c, z to indicate operations with single or double precision arithmetic on real or complex values.

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Acknowledgements

This work started in spring 2016 when Jose A. Belloch was a visiting postdoctoral researcher at Budapest University of Technology and Economics thanks to the European Network COST Action IC1305 inside the program Short Term Scientific Mission with the following reference: COST-SPASM-ECOST-STSM-IC1305-020416-072431. Dr. Jose A. Belloch is supported by GVA contract APOSTD/2016/069. The researchers from Universitat Jaume I are supported by the CICYT projects TIN2014-53495-R of MINECO and FEDER. The authors from the Universitat Politècnica de València are supported by MINECO Projects TEC2015-67387-C4-1-R, PROMETEOII/2014/003 and CAPAP-H5 network TIN2014-53522-REDT. The researcher from UCM is supported by the EU (FEDER) and the Spanish MINECO, under Grants TIN 2015-65277-R and TIN2012-32180. The work of Balázs Bank was supported by the ÚNKP-16-4-III New National Excellence Program of the Ministry of Human Capacities, Hungary.

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Belloch, J.A., Bank, B., Igual, F.D. et al. Solving Weighted Least Squares (WLS) problems on ARM-based architectures. J Supercomput 73, 530–542 (2017). https://doi.org/10.1007/s11227-016-1910-9

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Keywords

  • WLS
  • Audio processing
  • Low power processors
  • ARM\({}^{\circledR }\) Cortex