A Survey of Numerical Linear Algebra Methods Utilizing Mixed-Precision Arithmetic

Ahmad Abdelfattah, Hartwig Anzt, Erik Boman, Erin Carson, Terry Cojean, Jack Dongarra, Alyson Fox, Mark Gates, Nicholas Higham, Xiaoye Li, Jennifer Loe, Piotr Luszczek, Srikara Pranesh, Siva Rajamanickam, Tobias Ribizel, Barry Smith, Kasia Swirydowicz, Stephen Thomas, Stanimire Tomov, Yaohung TsaiUlrike Yang

Research output: Contribution to journalArticlepeer-review

59 Scopus Citations


The efficient utilization of mixed-precision numerical linear algebra algorithms can offer attractive acceleration to scientific computing applications. Especially with the hardware integration of low-precision special-function units designed for machine learning applications, the traditional numerical algorithms community urgently needs to reconsider the floating point formats used in the distinct operations to efficiently leverage the available compute power. In this work, we provide a comprehensive survey of mixed-precision numerical linear algebra routines, including the underlying concepts, theoretical background, and experimental results for both dense and sparse linear algebra problems.
Original languageAmerican English
Pages (from-to)344-369
Number of pages26
JournalInternational Journal of High Performance Computing Applications
Issue number4
StatePublished - 2021

NREL Publication Number

  • NREL/JA-2C00-77220


  • GPUs
  • high performance computing
  • linear algebra
  • mixed precision arithmetic
  • numerical mathematics


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