We construct a family of high order iteration functions for finding polynomial roots of a known multiplicity s. This family is a generalization of a fundamental family of high order algorithms for simple roots that dates back to Schröder’s 1870 paper. It starts with the well known variant of Newton’s method B̂2(x) = x − s · p(x)/p′(x) and the multiple root counterpart of Halley’s method derived ...

A recent iterative procedure by Lu et al. for designing IIR filters is recognized as the Sanathanan–Koerner or Steiglitz–McBride iteration, which was proposed originally in 1963 and 1965, respectively, for system identification purposes. We re-examine some claims and issues related to Lu et al.’s paper1 in view of various properties that have been deduced for the Steiglitz–McBride iteration in ...

The purpose of this article is to prove strong convergence theorems for fixed points of closed hemirelatively nonexpansive mappings. In order to get these convergence theorems, the monotone hybrid iteration method is presented and is used to approximate those fixed points. Note that the hybrid iteration method presented by S. Matsushita and W. Takahashi can be used for relatively nonexpansive m...

Greedy algorithms are often the first algorithm that one considers for various optimization problems, and ,in particular, covering problems. The idea is very simple: try to build a solution incrementally by augmenting a partial solution. In each iteration, select the “best” augmentation according to a simple criterion. The term greedy is used because the most common criterion is to select an au...

We present a new algorithm, incremental least squares policy iteration (ILSPI), for finding the infinite-horizon policy for partially observable Markov decision processes (POMDPs). The ILSPI algorithm computes a basis representation of the value function by minimizing the Bellman residual and it performs policy improvement in reachable belief states. A number of optimal basis functions are dete...

in this paper, we have proposed a new iterative method for finding the solution of ordinary differential equations of the first order. in this method we have extended the idea of variational iteration method by changing the general lagrange multiplier which is defined in the context of the variational iteration method.this causes the convergent rate of the method increased compared with the var...