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On Superlinear Convergence of Some Stable Variants of the Secant Method
Author(s) -
Burdakov O. P.
Publication year - 1986
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19860661212
Subject(s) - jacobian matrix and determinant , mathematics , secant method , convergence (economics) , nonlinear system , property (philosophy) , type (biology) , matrix (chemical analysis) , local convergence , newton's method , mathematical optimization , iterative method , ecology , philosophy , physics , materials science , epistemology , quantum mechanics , economics , composite material , biology , economic growth
In a recent author's paper four classes of methods of the secant type for solving systems of nonlinear equations were proposed. They are stable with respect to linear dependence of the search directions. If the Jacobian matrix is symmetric, then two of them take into account this property. It is proved here that some four special methods from the classes converge superlinearly.