A solution to the inverse boundary value problem of heat conduction posed in a new way

An iteration algorithm for solving the nonlinear inverse boundary value problem of heat conduction is proposed which makes it possible to allow for the results of temperature measurements at an arbitrary number of points inside the body. The iteration procedure proposed here is based on a conjugate gradient scheme. The gradient of the functional to be minimized is calculated from a formula based on a solution to the coupled boundary value problem; the descent step is estimated from a solution to the boundary value problem for temperature variations. The convergence and stability of the algorithm are estimated as a function of the number of temperature measurement points.