Geodesic
Convergence analysis of an optimization algorithm for computing
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XX, Tome 346 (2007), pp. 5-20

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A new optimization algorithm for computing the largest eigenvalue of a real symmetric matrix is considered. The algorithm is based on a sequence of plane rotations increasing the sum of the matrix entries. It is proved that the algorithm converges linearly and it is shown that it can be regarded as a relaxation method for the Rayleigh quotient. 
@article{ZNSL_2007_346_a0,
     author = {A. N. Borzykh},
     title = {Convergence analysis of an optimization algorithm for computing},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--20},
     publisher = {mathdoc},
     volume = {346},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_346_a0/}
}
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A. N. Borzykh. Convergence analysis of an optimization algorithm for computing. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XX, Tome 346 (2007), pp. 5-20. http://geodesic.mathdoc.fr/item/ZNSL_2007_346_a0/