By Curtis F. Gerald Patrick O. Wheatley
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Fraser and Hart  in 1962, Werner  in 1962 and Stoer  in 1964 gave methods based on solving the system of nonlinear equations directly. In 1966, Curtis and Osborne  gave an algorithm which used the eigenvalue connection explicitly, solving the eigenvalue problem by inverse iteration with zero as an initial estimate for the eigenvalue; they also established quadratic convergence. Breuer  in 1987 suggested a di erent direct approach to this subproblem which used continued fraction interpolation, and which it was claimed can lead to a considerable increase in e ciency, and also accuracy and robustness.