A gradient method of defining smooth solutions to inverse boundary-value problems in thermal conduction

An iterative algorithm is described for solving boundary-value inverse problems in thermal conduction by steepest descent, which utilizes information on the smoothness of the solution.Notation A, B linear operators - u element of solution space U - f exact reference data - f reference data uncertainty - value of reference data uncertainty - A^–1 inverse operator - u^(k)() k-th derivative of function u - _m length of observation interval - _i(t) polynomials of degree i–1 - A^*, B^*, L^* operators conjugate to the operators A, B, L - Jg discrepancy functional gradient - _n descent step along the discrepancy antigradient for the n-th iteration - K( –) kernel of integral equation - q() heat flux - T() measured temperature inside body Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 2, pp. 259–263, August, 1980.