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SUMMARY:Disentangling complexity in Bayesian automatic adaptive quadrature
DTSTART;VALUE=DATE-TIME:20170705T060000Z
DTEND;VALUE=DATE-TIME:20170705T063000Z
DTSTAMP;VALUE=DATE-TIME:20190325T201127Z
UID:indico-contribution-15@cern.ch
DESCRIPTION:Speakers: Prof. ADAM\, Gheorghe (LIT-JINR and IFIN-HH\, Buchar
est\, Romania)\nThe present report discusses a Bayesian automatic adaptive
quadrature (BAAQ) solution for numerical integration which is simultaneou
sly robust\, reliable\, and efficient\, hence able to yield guaranteed out
put in numerical experiments involving sudden unexpected modifications of
the behavior of the integrand function.\nAn essential ingredient of the so
lution is the multiscale approach [1]. Within it\, for integration ranges
of macroscopic length\, which are of primary practical interest\, an early
decision path for the integrand profile (IP) scrutiny is defined which en
ables fast solution of four basic problems: (i) identification of simple i
ntegrals\; (ii) check of the need to relax the user requested accuracy par
ameters\; (iii) end of computation diagnostic for simple integrals\; (iv)
hints on manifestly ill-conditioning IP features.\nFor integrals which are
neither trivial\, nor manifestly ill-conditioned\, the Clenshaw-Curtis qu
adrature is activated within the approach discussed in [2]. This enables f
urther identification of unresolved ill-conditioning features. We are thus
left either with a hopefully well-conditioned integral\, for which the st
andard automatic adaptive quadrature [3] is expected to yield reliable out
put\, or with a manifestly ill-conditioned problem for which an improved v
ersion of the full BAAQ machinery [4] is activated.\n\nReferences\n[1] Gh.
Adam\, S. Adam\, “Length Scales in Bayesian Automatic Adaptive Quadratu
re”\, in EPJ Web of Conferences\, vol. 108\, 2016\, 02002\, 1-6\; DOI: 1
0.1051/epjconf/201610802002. \n[2] S. Adam\, Gh. Adam\, “Summation Paths
in Clenshaw-Curtis Quadrature”\, in EPJ Web of Conferences\, vol. 108\,
2016\, 02003\, 1-6\; DOI: 10.1051/epjconf/201610802003.\n[3] A.R. Krommer
and C.W. Ueberhuber\, Computational Integration SIAM\, Philadelphia\, 199
8.\n[4] Gh. Adam and S. Adam\, in Mathematical Modeling and Computational
Science (MMCP2011)\, Gh. Adam\, J. Buša\, and M. Hnatič (Eds.)\, Springe
r\, Heidelberg\, LNCS 7125\, (2012) pp.1–16.\n\nhttps://indico.jinr.ru/c
ontributionDisplay.py?contribId=15&sessionId=1&confId=137
LOCATION: LIT Conference Hall
URL:https://indico.jinr.ru/contributionDisplay.py?contribId=15&sessionId=1
&confId=137
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