The paper presents a new approach of solving the initial-boundary heat conduction problems containing data subject to uncertainties. When the mathematical model contains measurement results, using the adjustment procedure, we can verify its accuracy and determine the influence of the measurement errors on the solution. The adjustment procedure is very often based upon the least squares principle. The constraint equations are usually derived using numerical methods. The coefficient matrix of the set of constraint equations is then a sparse matrix. We exploited the structure of this matrix and derived the multistage-multigroup method (MM method). The method was tested on the estimation of unsteady-state temperature fields in boiler shells. Both overdetermined and ill-posed cases are considered.
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