Mixed precision Rayleigh quotient iteration for total least squares problems
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10469268" target="_blank" >RIV/00216208:11320/23:10469268 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=_0zjReMaz0" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=_0zjReMaz0</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11075-023-01665-z" target="_blank" >10.1007/s11075-023-01665-z</a>
Alternative languages
Result language
angličtina
Original language name
Mixed precision Rayleigh quotient iteration for total least squares problems
Original language description
With the recent emergence of mixed precision hardware, there has been a renewed interest in its use for solving numerical linear algebra problems fast and accurately. The solution of total least squares problems, i.e., solving {$min_{E,r} | [E, r]|_F$} subject to $(A+E)x=b+${$r$}, arises in numerous applications. Solving this problem requires finding the smallest singular value and corresponding right singular vector of $[A,b]$, which is challenging when $A$ is large and sparse. An efficient algorithm for this case due to Bj"{o}rck et al. [SIAM J. Matrix Anal. Appl. 22(2), 2000], called RQI-PCGTLS, is based on Rayleigh quotient iteration coupled with the preconditioned conjugate gradient method.We develop a mixed precision variant of this algorithm, RQI-PCGTLS-MP, in which up to three different precisions can be used. We assume that the lowest precision is used in the computation of the preconditioner, and give theoretical constraints on how this precision must be chosen to ensure stability. In contrast to standard least squares, for total least squares, the resulting constraint depends not only on the matrix $A$, but also on the right-hand side $b$. We perform a number of numerical experiments on model total least squares problems used in the literature, which demonstrate that our algorithm can attain the same accuracy as RQI-PCGTLS albeit with a potential convergence delay due to the use of low precision. Performance modeling shows that the mixed precision approach can achieve up to a $4times$ speedup depending on the size of the matrix and the number of Rayleigh quotient iterations performed.
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
S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Numerical Algorithms
ISSN
1017-1398
e-ISSN
1572-9265
Volume of the periodical
2023
Issue of the periodical within the volume
05/10/2023
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
22
Pages from-to
—
UT code for WoS article
001079117400001
EID of the result in the Scopus database
2-s2.0-85173767553