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The backward heat conduction problem with variable coefficients in a spherical domain was considered. This problem is ill-posed, i.e., the solution (if it exists) to this problem does not depend continuously on the measured data. A projected iteration regularization method was constructed to obtain the regularized approximate solution to this inverse problem, and the convergence error estimates between the exact solution and the corresponding regularized approximate solution were given under the a priori and a posteriori parameter choice rules. Numerical results verify the effectiveness of this method. [ABSTRACT FROM AUTHOR]