# A short philosophical note on the origin of smoothed aggregations

Fraňková, Pavla; Hanuš, Milan; Kopincová, Hana; Kužel, Roman; Vaněk, Petr; Vastl, Zbyněk

- Applications of Mathematics 2013, Publisher: Institute of Mathematics AS CR(Prague), page 67-76

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topFraňková, Pavla, et al. "A short philosophical note on the origin of smoothed aggregations." Applications of Mathematics 2013. Prague: Institute of Mathematics AS CR, 2013. 67-76. <http://eudml.org/doc/287823>.

@inProceedings{Fraňková2013,

abstract = {We derive the smoothed aggregation two-level method from the variational objective to minimize the final error after finishing the entire iteration. This contrasts to a standard variational two-level method, where the coarse-grid correction vector is chosen to minimize the error after coarse-grid correction procedure, which represents merely an intermediate stage of computing. Thus, we enforce the global minimization of the error. The method with smoothed prolongator is thus interpreted as a qualitatively different, and more optimal, algorithm than the standard multigrid.},

author = {Fraňková, Pavla, Hanuš, Milan, Kopincová, Hana, Kužel, Roman, Vaněk, Petr, Vastl, Zbyněk},

booktitle = {Applications of Mathematics 2013},

keywords = {two-level method; pre-smoothing; coarse-grid correction; post-smoothing; error propagation; non-scalar elliptic problems; system of linear algebraic equations; symmetric positive definite matrix; smoothing; algorithms; aggregation method},

location = {Prague},

pages = {67-76},

publisher = {Institute of Mathematics AS CR},

title = {A short philosophical note on the origin of smoothed aggregations},

url = {http://eudml.org/doc/287823},

year = {2013},

}

TY - CLSWK

AU - Fraňková, Pavla

AU - Hanuš, Milan

AU - Kopincová, Hana

AU - Kužel, Roman

AU - Vaněk, Petr

AU - Vastl, Zbyněk

TI - A short philosophical note on the origin of smoothed aggregations

T2 - Applications of Mathematics 2013

PY - 2013

CY - Prague

PB - Institute of Mathematics AS CR

SP - 67

EP - 76

AB - We derive the smoothed aggregation two-level method from the variational objective to minimize the final error after finishing the entire iteration. This contrasts to a standard variational two-level method, where the coarse-grid correction vector is chosen to minimize the error after coarse-grid correction procedure, which represents merely an intermediate stage of computing. Thus, we enforce the global minimization of the error. The method with smoothed prolongator is thus interpreted as a qualitatively different, and more optimal, algorithm than the standard multigrid.

KW - two-level method; pre-smoothing; coarse-grid correction; post-smoothing; error propagation; non-scalar elliptic problems; system of linear algebraic equations; symmetric positive definite matrix; smoothing; algorithms; aggregation method

UR - http://eudml.org/doc/287823

ER -

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