Independent Loops Search in Flow Networks Aiming for Well-Conditioned System of Equations

Humaloja, Jukka-Pekka; Ali-Löytty, Simo; Pohjolainen, Seppo; Hämäläinen, Timo (2017)
 
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https://www.springer.com/gp/book/9783319630816


Humaloja, Jukka-Pekka
Ali-Löytty, Simo
Pohjolainen, Seppo
Hämäläinen, Timo
2017

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doi:10.1007/978-3-319-63082-3
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https://urn.fi/URN:NBN:fi:tty-201710182012

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We approach the problem of choosing linearly independent loops in a pipeflow network as choosing the best-conditioned submatrix of a given larger matrix. We present some existing results of graph theory and submatrix selection problems, based on which we construct three heuristic algorithms for choosing the loops. The heuristics are tested on two pipeflow networks that differ significantly on the distribution of pipes and nodes in the network.
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