Search results for "Nonlinear problems"
showing 2 items of 2 documents
Avoiding strange attractors in efficient parametric families of iterative methods for solving nonlinear problems
2019
[EN] Searching zeros of nonlinear functions often employs iterative procedures. In this paper, we construct several families of iterative methods with memory from one without memory, that is, we have increased the order of convergence without adding new functional evaluations. The main aim of this manuscript yields in the advantage that the use of real multidimensional dynamics gives us to decide among the different classes designed and, afterwards, to select its most stable members. Moreover, we have found some elements of the family whose behavior includes strange attractors of different kinds that must be avoided in practice. In this sense, Feigenbaum diagrams have resulted an extremely …
A posteriori error identities for nonlinear variational problems
2015
A posteriori error estimation methods are usually developed in the context of upper and lower bounds of errors. In this paper, we are concerned with a posteriori analysis in terms of identities, i.e., we deduce error relations, which holds as equalities. We discuss a general form of error identities for a wide class of convex variational problems. The left hand sides of these identities can be considered as certain measures of errors (expressed in terms of primal/dual solutions and respective approximations) while the right hand sides contain only known approximations. Finally, we consider several examples and show that in some simple cases these identities lead to generalized forms of the …