Abstract:
The paper shows how we can reformulate the inverse problem, which is solved by optimization method. The approach is demonstrated on four models of inverse problems. It is shown that when the inverse problem is the coecient problem, the use of parallel computing can reduce almost half of the time of the inverse problem's numerical solution calculating, as solving direct and conjugate problems can be searched in parallel way. If the inverse problem is linear (the unknown boundary condition or the right side of an equation are being looked for),then the inverse problem can be reduced to the numerical solution of the moment problem, for which all the necessary functions can be computed in advance by the known data of the inverse problem. To illustrate the proposed approach, we represent the numerical solution of the Cauchy problem for an elliptic equation on data obtained from the physical experiment.
Keywords:coecient hyperbolic inverse problem, retrospective inverse problem of heat conduction, the Cauchy problem for an elliptic equation, denition of the function of an elliptic equation source, optimization method, conjugate problem, residual functional, problem of moments.
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