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In [1], a method is suggested, in a rather implicit way, by which an illconditioned symmetric system of linear algebraic equations is "improved" by replacing a row of the coefficient matrix by an eigenvector. In this paper, this method is described and investigated, the best choices of parameters are recommended, and estimates of the improvement archieved are given.
[1] J. W. Head G. M. Oulton: The Solution of "Ill-conditioned" Linear Simultaneous Equations. Aircraft Engineering, Vol. XXX, 1958, Math., 309-312. MR 0095581
[2] Ф. Р. Гаитмахер: Теория матриц. Изд. Наука, Москва 1966. Zbl 1155.78304
[3] J. H. Wilkinson: Sounding Errors in Algebraic Processes. London, H. M. Stationery Office, 1963. MR 0161456
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