Reports de recerca http://hdl.handle.net/2117/3603 2022-01-17T03:33:58Z A technique to composite a modified Newton's method for solving nonlinear equations http://hdl.handle.net/2117/12477 A technique to composite a modified Newton's method for solving nonlinear equations Grau Sánchez, Miguel; Díaz Barrero, José Luis A zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is improved is presented. The key idea in deriving this procedure is to compose a given iterative method with a modified Newton’s method that introduces just one evaluation of the function. To carry out this procedure some classical methods with different orders of convergence are used to obtain root-finders with higher efficiency index. Nova tècnica que permet construir mètodes iteratius d'ordre alt. 2011-05-05T11:44:52Z Grau Sánchez, Miguel Díaz Barrero, José Luis A zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is improved is presented. The key idea in deriving this procedure is to compose a given iterative method with a modified Newton’s method that introduces just one evaluation of the function. To carry out this procedure some classical methods with different orders of convergence are used to obtain root-finders with higher efficiency index. On computational order of convergence of some multi-precision solvers of nonlinear systems of equations http://hdl.handle.net/2117/12475 On computational order of convergence of some multi-precision solvers of nonlinear systems of equations Grau Sánchez, Miguel; Grau Gotés, Maria Àngela; Díaz Barrero, José Luis In this paper the local order of convergence used in iterative methods to solve nonlinear systems of equations is revisited, where shorter alternative analytic proofs of the order based on developments of multilineal functions are shown. Most important, an adaptive multi-precision arithmetics is used hereof, where in each step the length of the mantissa is defined independently of the knowledge of the root. Furthermore, generalizations of the one dimensional case to m-dimensions of three approximations of computational order of convergence are defined. Examples illustrating the previous results are given. Report d'un treball de recerca on es presenten noves tècniques de càlcul de l'ordre de convergència amb una aritmètica adaptativa. 2011-05-05T11:25:05Z Grau Sánchez, Miguel Grau Gotés, Maria Àngela Díaz Barrero, José Luis In this paper the local order of convergence used in iterative methods to solve nonlinear systems of equations is revisited, where shorter alternative analytic proofs of the order based on developments of multilineal functions are shown. Most important, an adaptive multi-precision arithmetics is used hereof, where in each step the length of the mantissa is defined independently of the knowledge of the root. Furthermore, generalizations of the one dimensional case to m-dimensions of three approximations of computational order of convergence are defined. Examples illustrating the previous results are given.