An inverse problem for a discrete Dirac system (Q1975106)

The author proposes an algorithm for the numerical solution of an inverse problem for a discrete Dirac system. The problem is reduced to constructing a symmetric tridiagonal matrix with given distinct eigenvalues and given symmetry conditions for the eigenvectors. An orthonormalized basis of eigenvectors is calculated simultaneously with the matrix. The Lanczos method with additional complete orthonormalization gives good results even for high-order \((N=1000)\) matrices. A partial orthonormalization results in oscillations that essentially distort a solution.