Solving the eigenvalue problem for matrices

One presents some algorithms related among themselves for solving the partial and the complete eigenvalue problem for an arbitrary matrix. Algorithm 1 allows us to construct the invariant subspaces and to obtain with their aid a matrix whose eigenvalues coincide with the eigenvalues of the initial matrix and belong to a given semiplane. Algorithm 2 solves the same problem for a given strip. The algorithms 3 and 4 reduces the complete eigenvalue problem of an arbitrary matrix to some problem for a quasitriangular matrix whose diagonal blocks have eigenvalues with identical real parts. Algorithm 4 finds also the unitary matrix which realizes this transformation. One gives Algol programs which realize the algorithms 1–3 for real matrices and testing examples.