The solution of the additive eigenvalue problem of matrices

It is required to determine a diagonal matrix X such that the symmetric matrix A+X has preassigned eigenvalues (the additive problem). An iteration process is described that is based on the use of two-dimensional rotations, and convergence problems are analyzed.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 48, pp. 12–17, 1974.