Geodesic
Solving the eigenvalue problem for matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms, Tome 70 (1977), pp. 124-139

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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. 
@article{ZNSL_1977_70_a7,
     author = {V. N. Kublanovskaya and L. T. Savinova},
     title = {Solving the eigenvalue problem for matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {124--139},
     publisher = {mathdoc},
     volume = {70},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1977_70_a7/}
}
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V. N. Kublanovskaya; L. T. Savinova. Solving the eigenvalue problem for matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms, Tome 70 (1977), pp. 124-139. http://geodesic.mathdoc.fr/item/ZNSL_1977_70_a7/