@Article{Amat2003, author="S. Amat, S. Busquier", title=" On a higher order Secant method", journal=" Appl. Math. Comput.", year="2003", pages=" 321–329. ", volume="141" } @Article{Amat2004, author=" S. Amat, S. Busquier, M. Negra", title=" Adaptive approximation of nonlinear operators", journal=" Numer. Funct. Anal. Optim.", year="2004", pages="397–405.", volume="25" } @Article{Amat2014, author="S. Amat, J. A. Ezquerro, M. A. Hernández-Vern", title=" Approximation of inverse operators by a new family of high-order iterative methods", journal=" Numer. Linear Algebra Appl.", year="2014", pages="629–664. ", volume="21" } @Article{Amat2014, author="S. Amat, M. A. Hernández-Vern, M. J. Rubio", title=" Improving the applicability of the Secant method to solve nonlinear systems of equations", journal="Appl. Math. Comput.", year="2014", pages="741–752.", volume="247" } @Book{Argyros2007, author="I. K. Argyros", title="Computational theory of iterative methods", year="2007", publisher="Elsevier B. V.", address="Amsterdam" } @Book{Argyros2012, author="I. K. Argyros, Y. J. Cho, S. Hilout ", title="Numerical method for equations and its applications", year="2012", publisher="CRC Press", address="Boca Raton" } @Article{Argyros2014, author="I. K. Argyros, D. González, Á . A. Magreñán ", title="A semilocal convergence for a uniparametric family of efficient Secant-like methods ", journal="J. Funct. Spaces", year="2014", pages="10 pages. ", volume="2014" } @Article{Argyros2012, author=" I. K. Argyros, S. Hilout", title="Weaker conditions for the convergence of Newton’s method ", journal="J. Complexity", year="2012", pages="364–387.", volume="28" } @Article{Argyros2014, author="I. K. Argyros, Á . A. Magreñán ", title="A unified convergence analysis for secant-type methods ", journal="J. Korean Math. Soc.", year="2014", pages="1155–1175. ", volume="51" } @Article{Argyros2015, author="I. K. Argyros, Á . A. Magreñán", title="Expanding the applicability of the secant method under weaker conditions ", journal="Appl. Math. Comput.", year="2015", pages="1000–1012.", volume="266" } @Article{Argyros2014, author="I. K. Argyros, Á . A. Magreñán", title="Relaxed Secant-type methods", journal="Nonlinear Stud.", year="2014", pages="485–503.", volume="21" } @Article{Cătinaş 2005, author="E. Cătinaş ", title="The inexact, inexact perturbed, and quasi-Newton methods are equivalent models", journal="Math. Comp.", year="2005", pages="291–301.", volume="74" } @Book{Chandrasekhar1960, author="S. Chandrasekhar", title="Radiative transfer", year="1960", publisher="Dover Publ.", address="New York" } @Article{Dennis1970, author="J. E. Dennis", title="Toward a unified convergence theory for Newton-like methods", journal="Nonlinear Functional Anal. and Appl.", year="1970", pages="425–472.", volume="1970" } @Article{Ezquerro2010, author="J. A. Ezquerro, J. M. Gutiérrez, M. A. Hernández, N. Romero, M. J. Rubio", title="The Newton method: from Newton to Kantorovich (Spanish)", journal="Gac. R. Soc. Mat. Esp.", year="2010", pages="53–76. ", volume="13" } @Article{Farhane2017, author="N. Farhane, I. Boumhidi, J. Boumhidi", title="Smart Algorithms to Control a Variable Speed Wind Turbine", journal="Int. J. Interact. Multimed. Artif. Intell.", year="2017", pages="88–95.", volume="4" } @Article{Gragg1974, author="W. B. Gragg, R. A. Tapia", title="Optimal error bounds for the Newton-Kantorovich theorem", journal="SIAM J. Numer. Anal.", year="1974", pages="10–13. ", volume="11" } @Article{Hernández2000, author="M. A. Hernández, M. J. Rubio, J. A. Ezquerro ", title="Secant-like methods for solving nonlinear integral equations of the Hammerstein type", journal="J. Comput. Appl. Math.", year="2000", pages="245–254.", volume="115" } @Article{Jain2013, author="D. Jain", title="Families of Newton-like methods with fourth-order convergence", journal="Int. J. Comput. Math.", year="2013", pages="1072–1082.", volume="90" } @Book{Kantorovich1982, author="L. V. Kantorovich, G. P., Akilov", title="Functional Analysis (Translated from the Russian by Howard L. Silcock)", year="1982", publisher="Pergamon Press", address="Oxford-Elmsford" } @Article{Kaur2017, author="R. Kaur, S. Arora", title="Nature Inspired Range BasedWireless Sensor Node Localization Algorithms", journal="Int. J. Interact. Multimed. Artif. Intell.", year="2017", pages="7–17. ", volume="4" } @Article{Magreñán2014, author="Á . A. Magreñán", title="A new tool to study real dynamics: The convergence plane", journal="Appl. Math. Comput.", year="2014", pages="215–224.", volume="248" } @Book{Ortega1970, author="J. M. Ortega, W. C. Rheinboldt", title="Iterative Solution of Nonlinear Equations in Several Variables", year="1970", publisher="Academic press ", address="" } @Book{Potra1984, author="F. A. Potra, V. Pták", title="Nondiscrete induction and iterative processes", year="1984", publisher="Pitman (Advanced Publishing Program)", address="Boston" } @Article{Proinov2009, author="P. D. Proinov", title="General local convergence theory for a class of iterative processes and its applications to Newton’s method ", journal="J. Complexity", year="2009", pages="38–62. ", volume="25" } @Article{Rheinboldt1975, author="W. C. Rheinboldt", title="An adaptative continuation process for solving systems of nonlinear equations", journal="Banach Ctz. Publ.", year="1975", pages="129–142.", volume="3" } @Article{Schmidt1978, author="J. W. Schmidt", title="Untere fehlerschranken fr regula-falsi-verfahren", journal="Period. Hungar.", year="1978", pages="241–247. ", volume="9" } @Book{Traub 1964, author="J. F. Traub ", title="Iterative method for solutions of equations", year="1964", publisher="Prentice-Hall", address="Englewood Cliffs" } @Article{Yamamoto1987, author="T. Yamamoto", title=" A convergence theorem for Newton-like methods in Banach spaces", journal="Numer. Math.", year="1987", pages="545–557.", volume="51" } @Article{Zabrejko1987, author="P. P. Zabrejko, D. F. Nguen", title="The majorant method in the theory of Newton-Kantorovich approximations and the Pták error estimates", journal="Numer. Funct. Anal. Optim.", year="1987", pages="671–684.", volume="9" }