All

What are you looking for?

All
Projects
Results
Organizations

Quick search

  • Projects supported by TA ČR
  • Excellent projects
  • Projects with the highest public support
  • Current projects

Smart search

  • That is how I find a specific +word
  • That is how I leave the -word out of the results
  • “That is how I can find the whole phrase”

Mixed precision s-step Lanczos and conjugate gradient algorithms

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10436238" target="_blank" >RIV/00216208:11320/21:10436238 - isvavai.cz</a>

  • Result on the web

    <a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=6NE8Dz.9PD" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=6NE8Dz.9PD</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1002/nla.2425" target="_blank" >10.1002/nla.2425</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Mixed precision s-step Lanczos and conjugate gradient algorithms

  • Original language description

    Compared to the classical Lanczos algorithm, the s-step Lanczos variant has the potential to improve performance by asymptotically decreasing the synchronization cost per iteration. However, this comes at a price; despite being mathematically equivalent, the s-step variant may behave quite differently in finite precision, potentially exhibiting greater loss of accuracy and slower convergence relative to the classical algorithm. It has previously been shown that the errors in the s-step version follow the same structure as the errors in the classical algorithm, but are amplified by a factor depending on the square of the condition number of the O(s)-dimensional Krylov bases computed in each outer loop. As the condition number of these s-step bases grows (in some cases very quickly) with s, this limits the s values that can be chosen and thus can limit the attainable performance. In this work, we show that if a select few computations in s-step Lanczos are performed in double the working precision, the error terms then depend only linearly on the conditioning of the s-step bases. This has the potential for drastically improving the numerical behavior of the algorithm with little impact on per-iteration performance. Our numerical experiments demonstrate the improved numerical behavior possible with the mixed precision approach, and also show that this improved behavior extends to mixed precision s-step CG. We present preliminary performance results on NVIDIA V100 GPUs that show that the overhead of extra precision is minimal if one uses precisions implemented in hardware.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    10102 - Applied mathematics

Result continuities

  • Project

  • Continuities

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2021

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Numerical Linear Algebra with Applications

  • ISSN

    1070-5325

  • e-ISSN

  • Volume of the periodical

    2021

  • Issue of the periodical within the volume

    e2425

  • Country of publishing house

    GB - UNITED KINGDOM

  • Number of pages

    24

  • Pages from-to

    1-24

  • UT code for WoS article

    000721446000001

  • EID of the result in the Scopus database

    2-s2.0-85119656079