A Note on Iterative Refinement for Seminormal Equations
Result 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.
Keywords
The result's identifiers
Result code in IS VaVaI
Alternative codes found
RIV/46747885:24220/14:#0003155
Result on the web
DOI - Digital Object Identifier
Alternative languages
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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Classification
Type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
GAP108/11/0853: Nanostructures with transition metals: Towards ab-initio material design
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Applied Numerical Mathematics
ISSN
0168-9274
e-ISSN
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Volume of the periodical
75
Issue of the periodical within the volume
January
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
8
Pages from-to
167-174
UT code for WoS article
000328298900013
EID of the result in the Scopus database
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Basic information
Result type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP
BA - General mathematics
Year of implementation
2014