Let f and g be two convergent power series in R[[z]] or C[[z]], whose first n terms are given numerically with a λ n-bit precision for a fixed constant λ> 0. Assuming that g0=0, we will show in this paper that the first n coefficients of f ◦ g can be computed with a λn-bit precision in time Õ(n). Using Newton iteration, a similar complexity bound holds for power series reversion of g. Our metho...

We prove the weak convergence of Mann iteration for a hybrid pair of maps to a common fixed point of a selfmap f and a multivalued f nonexpansive mapping T in Banach space E. Keywords—Common fixed point, Mann iteration, Multivalued mapping, weak convergence.

We study iterative multiuser detection in large randomly spread code division multiple access systems under the assumption that the number of users accessing the channel is unknown by the receiver. In particular, we focus on the factor graph representation and iterative algorithms based on belief propagation. We build an iterative scheme that detects the encoded data and the users’ activity. By...

We develop and compare multilevel algorithms for solving constrained nonlinear variational problems via interior point methods. Several equivalent formulations of the linear systems arising at each iteration of the interior point method are compared from the point of view of conditioning and iterative solution. Furthermore, we show how a multilevel continuation strategy can be used to obtain go...

Maximum likelihood estimations for the parameters of extreme value distributions are discussed in this paper using fixed point iteration. The commonly used numerical approach for adressing this problem is the Newton-Raphson approach which requires differentiation unlike the fixed point iteration which is also easier to implement. Graphical approaches are also usualy proposed in the literature. ...

We develop and compare multilevel algorithms for solving bound constrained nonlinear variational problems via interior point methods. Several equivalent formulations of the linear systems arising at each iteration of the interior point method are compared from the point of view of conditioning and iterative solution. Furthermore, we show how a multilevel continuation strategy can be used to obt...

We develop and compare multilevel algorithms for solving constrained nonlinear variational problems via interior point methods. Several equivalent formulations of the linear systems arising at each iteration of the interior point method are compared from the point of view of conditioning and iterative solution. Furthermore, we show how a multilevel continuation strategy can be used to obtain go...