Summary
Sharp a priori and a posteriori error bounds are given for the secant method for solving non-linear equations in Banach spaces. The numerical stability of this method is also investigated. The stability results are analogous to those obtained by Lancaster for Newton's method.
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Potra, F.A. An error analysis for the secant method. Numer. Math. 38, 427–445 (1982). https://doi.org/10.1007/BF01396443
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DOI: https://doi.org/10.1007/BF01396443