A Note on Iterative Refinement for Seminormal Equations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F14%3A00395951" target="_blank" >RIV/67985807:_____/14:00395951 - isvavai.cz</a>
Alternative codes found
RIV/46747885:24220/14:#0003155
Result on the web
<a href="http://dx.doi.org/10.1016/j.apnum.2013.08.005" target="_blank" >http://dx.doi.org/10.1016/j.apnum.2013.08.005</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.apnum.2013.08.005" target="_blank" >10.1016/j.apnum.2013.08.005</a>

Result language
angličtina
Original language name
A Note on Iterative Refinement for Seminormal Equations
Original language description
We present a roundoff error analysis of the method for solving the linear least squares problems with full column rank matrix using only the diagonal and right orthogonal factors from the SVD decomposition of the system matrix. This method is an analogueof the method of seminormal equations, where the solution is computed using only the triangular factor fom the QR factorization of A. We analyze one step of fixed precision iterative refinement to improve the accuracy of this method a we show that undercertain conditions, it produces a forward stable solution. However, it is generally not forward stable and has similar numerical properties to the corrected method of seminormal equations. We illustrate our analysis by numerical experiments.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/GAP108%2F11%2F0853" target="_blank" >GAP108/11/0853: Nanostructures with transition metals: Towards ab-initio material design</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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