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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Integral equations
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Numerical Treatment of Inverse Problems in Differential and Integral Equations - Proceedings of an International Workshop, Heidelberg, Fed. Rep. of Germany, August 30 - September 3, 1982 (Paperback, Softcover reprint of the original 1st ed. 1983)
Loot Price: R1,599
Discovery Miles 15 990
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Numerical Treatment of Inverse Problems in Differential and Integral Equations - Proceedings of an International Workshop, Heidelberg, Fed. Rep. of Germany, August 30 - September 3, 1982 (Paperback, Softcover reprint of the original 1st ed. 1983)
Series: Progress in Scientific Computing, 2
Expected to ship within 10 - 15 working days
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In many scientific or engineering applications, where ordinary
differen tial equation (OOE), partial differential equation (POE),
or integral equation (IE) models are involved, numerical simulation
is in common use for prediction, monitoring, or control purposes.
In many cases, however, successful simulation of a process must be
preceded by the solution of the so-called inverse problem, which is
usually more complex: given meas ured data and an associated
theoretical model, determine unknown para meters in that model (or
unknown functions to be parametrized) in such a way that some
measure of the "discrepancy" between data and model is minimal. The
present volume deals with the numerical treatment of such inverse
probelms in fields of application like chemistry (Chap. 2,3,4,
7,9), molecular biology (Chap. 22), physics (Chap. 8,11,20),
geophysics (Chap. 10,19), astronomy (Chap. 5), reservoir simulation
(Chap. 15,16), elctrocardiology (Chap. 14), computer tomography
(Chap. 21), and control system design (Chap. 12,13). In the actual
computational solution of inverse problems in these fields, the
following typical difficulties arise: (1) The evaluation of the sen
sitivity coefficients for the model. may be rather time and storage
con suming. Nevertheless these coefficients are needed (a) to
ensure (local) uniqueness of the solution, (b) to estimate the
accuracy of the obtained approximation of the solution, (c) to
speed up the iterative solution of nonlinear problems. (2) Often
the inverse problems are ill-posed. To cope with this fact in the
presence of noisy or incomplete data or inev itable discretization
errors, regularization techniques are necessary."
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