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We propose a globally convergent computational technique for the nonlinearinverse problem of reconstructing the zero-order coefficient in a parabolicequation using partial boundary data. This technique is called the "reduceddimensional method". Initially, we use the polynomial-exponential basis toapproximate the inverse problem as a system of 1D nonlinear equations. We thenemploy a Picard iteration based on the quasi-reversibility method and aCarleman weight function. We will rigorously prove that the sequence derivedfrom this iteration converges to the accurate solution for that 1D systemwithout requesting a good initial guess of the true solution. The key tool forthe proof is a Carleman estimate. We will also show some numerical examples.

A Carleman-Picard approach for reconstructing zero-order coefficients in parabolic equations with limited data