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Modeling and Inverse Problems in the Presence of Uncertainty
book

Modeling and Inverse Problems in the Presence of Uncertainty

by H. T. Banks, Shuhua Hu, W. Clayton Thompson
April 2014
Intermediate to advanced content levelIntermediate to advanced
405 pages
13h
English
Chapman and Hall/CRC
Content preview from Modeling and Inverse Problems in the Presence of Uncertainty
Mathematical and Statistical Aspects of Inverse Problems 73
that the matrix J or
˜
J must be positive semi- de finite, so that the assump-
tion (A7) or (A7
) may not be overly restrictive. Alternatively, as has been
noted before, one can relax the assumptions (A7) or (A7
) by assuming the
existence of a dominating function b. Moreover, provided the weights w(t)
satisfy the requirement w(t) ¯w > 0 for all t [t
0
, t
f
], then one can use the
dominating function b (from the ordinary least squares problem) to obtain a
new dominating function
˜
b(E, t) = ¯w
1
b(E, t) which is also ν-integrable. Even
in this case , though, one must still make the a dditio na
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Publisher Resources

ISBN: 9781482206432