Some Classes of third and Fourth-order iterative methods for solving nonlinear equations

The object of the present work is to present the new classes of third-order and fourth-order iterative methods for solving nonlinear equations. Our third-order method includes methods of Weerakoon \cite{Weerakoon}, Homeier \cite{Homeier2}, Chun \cite{Chun} e.t.c. as particular cases. After that we make this third-order method to fourth-order (optimal) by using a single weight function rather than using two different weight functions in \cite{Soleymani}. Finally some examples are given to illustrate the performance of the our method by comparing with new existing third and fourth-order methods.Comment: arXiv admin note: substantial text overlap with arXiv:1307.733

An O∗(1.0821n)O^*(1.0821^n)-Time Algorithm for Computing Maximum Independent Set in Graphs with Bounded Degree 3

We give an $O^*(1.0821^n)$-time, polynomial space algorithm for computing Maximum Independent Set in graphs with bounded degree 3. This improves all the previous running time bounds known for the problem