Solving large linear least squares problems with linear equality constraints

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10455908" target="_blank" >RIV/00216208:11320/22:10455908 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=xd3yR9sEn7" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=xd3yR9sEn7</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10543-022-00930-2" target="_blank" >10.1007/s10543-022-00930-2</a>

Result language
angličtina
Original language name
Solving large linear least squares problems with linear equality constraints
Original language description
We consider the problem of solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly.While some classical approaches are theoretically well founded, they can face difficultieswhen thematrix ofconstraints contains dense rows or if an algorithmic transformation used in the solution process results in a modified problem that is much denser than the original one. We propose modifications with an emphasis on requiring that the constraints be satisfiedwith a small residual.We examine combining the null-space method with our recently developed algorithm for computing a null-space basis matrix for a "wide" matrix.We further show that a direct elimination approach enhanced by careful pivoting can be effective in transforming the problem to an unconstrained sparse-dense least squares problem that can be solved with existing direct or iterative methods. We also present a number of solution variants that employ an augmented system formulation, which can be attractive for solving a sequence of related problems. Numerical experiments on problems coming from practical applications are used throughout to demonstrate the effectiveness of the different approaches.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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