Interpolatory multipoint methods with memory for solving nonlinear equations
Tài liệu tham khảo
Bi, 2009, A new family of eight-order iterative methods for solving nonlinear equations, Appl. Math. Comput., 214, 236, 10.1016/j.amc.2009.03.077
Bi, 2009, Three-step iterative methods with eight-order convergence for solving nonlinear equations, J. Comput. Appl. Math., 225, 105, 10.1016/j.cam.2008.07.004
Džunić, 2011, A family of optimal three-point methods for solving nonlinear equations using two parametric functions, Appl. Math. Comput., 217, 7612, 10.1016/j.amc.2011.02.055
Geum, 2010, A multi-parameter family of three-step eighth-order iterative methods locating a simple root, Appl. Math. Comput., 215, 3375, 10.1016/j.amc.2009.10.030
T. Granlund, GNU MP; The GNU Multiple Precision Arithmetic Library, edition 5.0.1, 2010.
Herzberger, 1974, Über Matrixdarstellungen für iterationverfahren bei nichtlinearen Gleichungen, Computing, 12, 215, 10.1007/BF02293107
Jarratt, 1966, Some fourth order multipoint methods for solving equations, Math. Comput., 20, 434, 10.1090/S0025-5718-66-99924-8
Jarratt, 1969, Some efficient fourth-order multipoint methods for solving equations, BIT, 9, 119, 10.1007/BF01933248
King, 1971, A fifth order family of modified Newton methods, BIT, 11, 409, 10.1007/BF01939409
King, 1973, A family of fourth order methods for nonlinear equations, SIAM J. Numer. Anal., 10, 876, 10.1137/0710072
Kung, 1974, Optimal order of one-point and multipoint iteration, J. ACM, 21, 643, 10.1145/321850.321860
Liu, 2010, Eighth-order methods with high efficiency index for solving nonlinear equations, Appl. Math. Comput., 215, 3449, 10.1016/j.amc.2009.10.040
Maheshwari, 2009, A fourth-order iterative method for solving nonlinear equations, Appl. Math. Comput., 211, 383, 10.1016/j.amc.2009.01.047
Neta, 1979, A sixth order family of methods for nonlinear equations, Int. J. Comput. Math., 7, 157, 10.1080/00207167908803166
Neta, 1981, On a family of multipoint methods for nonlinear equations, Int. J. Comput. Math., 9, 353, 10.1080/00207168108803257
Neta, 1983, A new family of higher order methods for solving equations, Int. J. Comput. Math., 14, 191, 10.1080/00207168308803384
Neta, 1988, Several new methods for solving equations, Int. J. Comput., 23, 265, 10.1080/00207168808803622
Neta, 2008, High order nonlinear solver, J. Comput. Methods Sci. Eng., 8, 245
Neta, 2010, Construction of optimal order nonlinear solvers using inverse interpolation, Appl. Math. Comput., 217, 2448, 10.1016/j.amc.2010.07.045
Ostrowski, 1960
Petković, 2010, On a general class of multipoint root-finding methods of high computational efficiency, SIAM J. Numer. Anal., 47, 4402, 10.1137/090758763
Petković, 2010, Derivative free two-point methods with and without memory for solving nonlinear equations, Appl. Math. Comput., 217, 1887, 10.1016/j.amc.2010.06.043
M.S. Petković, B. Neta, L.D. Petković, On the Kung-Traub family of multipoint methods with memory, private communication.
Petković, 2010, Families of optimal multipoint methods for solving nonlinear equations: a survey, Appl. Anal. Discrete Math., 4, 1, 10.2298/AADM100217015P
Petković, 2010, A class of three-point root-solvers of optimal order of convergence, Appl. Math. Comput., 216, 671, 10.1016/j.amc.2010.01.123
Ren, 2009, A class of two-step Steffensen type methods with fourth-order convergence, Appl. Math. Comput., 209, 206, 10.1016/j.amc.2008.12.039
Sharma, 2010, A new family of modified Ostrowskis methods with accelerated eighth order convergence, Numer. Algor., 54, 445, 10.1007/s11075-009-9345-5
Thukral, 2010, Family of three-point methods of optimal order for solving nonlinear equations, J. Comput. Appl. Math., 233, 2278, 10.1016/j.cam.2009.10.012
Traub, 1964
Wang, 2010, New eighth-order iterative methods for solving nonlinear equations, J. Comput. Appl. Math., 234, 1611, 10.1016/j.cam.2010.03.002
Yun, 2008, A non-iterative method for solving non-linear equations, Appl. Math. Comput., 198, 691, 10.1016/j.amc.2007.09.006
Yun, 2009, Iterative methods based on the signum function approach for solving nonlinear equations, Numer. Algor., 52, 649, 10.1007/s11075-009-9305-0