Geodesic
Stable versions of the secants method for solving systems of equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 23 (1983) no. 5, pp. 1027-1040

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An interpretation of quasi-Newton methods of solving sets of equations is given, and provides the basis of four versions of the secants method, stable with respect to a linear dependence of the directions of motion. The first version involves an approximation of the matrix of first derivatives (the Jacobi matrix), and the second an approximation of the inverse Jacobi matrix. The other two versions are aimed at solving sets of equations with symmetric Jacobi matrix. The stability of the versions is proved. 
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     author = {O. P. Burdakov},
     title = {Stable versions of the secants method for solving systems of equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     publisher = {mathdoc},
     volume = {23},
     number = {5},
     year = {1983},
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     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_5_a0/}
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O. P. Burdakov. Stable versions of the secants method for solving systems of equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 23 (1983) no. 5, pp. 1027-1040. http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_5_a0/