Stochastic regularization for thermal problems with uncertain parameters

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Abstract
Usually when determining parameters with an inverse method, it is assumed that parameters or properties, other than those being sought, are known exactly. When such known parameters are uncertain, the inverse solution can be very sensitive to the degree of uncertainty. This paper presents a modification to the least squares technique which reduces the sensitivity to the uncertainty in the known parameters. In the presence of noisy data the method can be improved slightly by using Tikhanov's regularization. The reason for this limited improvement can be understood by examining the stochastic regularization method.