Geodesic
The gradient-based method for solving the inverse coefficient heat-conduction problem
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 11 (2008) no. 1, pp. 41-51

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An iterative gradient descent method has been applied to the inverse coefficient heat-conduction problem with overdetermined boundary conditions. Some theoretical estimates have been obtained for variation of the target functional with respect to the variation of the coefficient. Using these estimates, an approximated gradient of the target functional has been constructed. In the numerical experiments, the iteration convergence rates for different gradient descent parameters were compared. 
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     author = {S. I. Kabanikhin and A. Kh. Khasanov and A. V. Penenko},
     title = {The gradient-based method for solving the inverse coefficient heat-conduction problem},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {41--51},
     publisher = {mathdoc},
     volume = {11},
     number = {1},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2008_11_1_a3/}
}
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S. I. Kabanikhin; A. Kh. Khasanov; A. V. Penenko. The gradient-based method for solving the inverse coefficient heat-conduction problem. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 11 (2008) no. 1, pp. 41-51. http://geodesic.mathdoc.fr/item/SJVM_2008_11_1_a3/