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SUMMARY:Acceleration of sequential subspace optimization in Banach spaces
by orthogonal search directions
DTSTART;VALUE=DATE-TIME:20191107T140000Z
DTEND;VALUE=DATE-TIME:20191107T144000Z
DTSTAMP;VALUE=DATE-TIME:20200808T235038Z
UID:indico-contribution-40@conference2.aau.at
DESCRIPTION:Speakers: Thomas Schuster ()\nA standard solution technique fo
r linear operator equations of first kind is the Landweber scheme which is
an iterative method that uses the negative gradient of the current residu
al as search direction\, which is then also called the Landweber direction
. Though this method proves to be stable with respect to noisy data\, it i
s known to be numerically slow for problems in Hilbert spaces and this beh
avior shows to be even worse in some Banach space settings. This is why th
e idea came up to use several search directions instead of the Landweber d
irection only which has led to the development of Sequential Subspace Opti
mization (SESOP) methods. This idea is related to Conjugate Gradient (CG)
techniques that are known to be amongst the most effective methods to solv
e linear equations in Hilbert spaces. SESOP methods in Banach spaces do no
t share the conjugacy property with CG methods. In this talk we present th
e concept of generalized (g-)orthogonality in Banach spaces and apply metr
ic projections to orthogonalize the current Landweber direction with respe
ct to the search space of the last iteration. This leads to an accelerated
SESOP method which is confirmed by various numerical experiments.\n(joine
d work with Frederik Heber and Frank Schoepfer)\n\nhttps://conference2.aau
.at/event/16/contributions/40/
LOCATION:Stiftungssaal K.0.01
URL:https://conference2.aau.at/event/16/contributions/40/
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