A numerical solution to a problem of crystal energy spectrum determination by the heat capacity dependent on a temperature

The paper consider an important practical problem of determining the phonon spectrum of a crystal by the heat capacity dependent on temperature. The problem reduces to an integral equation of the first kind solvable by the regularizing algorithm. This algo- rithm involves finite-dimensional approximation of the original problem and allows reducing the problem to a system of linear algebraic equations by use of the Tikhonov regularization method. The approximate solution accuracy accounting for the error of the finite-dimensional problem approximation has been estimated.