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In this paper, we consider simultaneous reconstruction of the diffusioncoefficient and initial state for a one-dimensional heat equation throughboundary control and measurement. The boundary measurement is known to make thesystem exactly observable, and both coefficient and initial state are shown tobe identifiable by this measurement. By a Dirichlet series representation forobservation, we can transform the problem into an inverse process ofreconstruction of the spectrum and coefficients for Dirichlet series in termsof observation. This happens to be the reconstruction of spectral data for anexponential sequence with measurement error. This enables us to develop analgorithm based on the matrix pencil method in signal analysis. An erroranalysis is made for the proposed method. The numerical simulations arepresented to verify the proposed algorithm.

Simultaneous Identification of Coefficient and Initial State for One-Dimensional Heat Equation from Boundary Control and Measurement