a systematic way is presented for the construction of multi-step iterative method with frozen jacobian. the inclusion of an auxiliary function is discussed. the presented analysis shows that how to incorporate auxiliary function in a way that we can keep the order of convergence and computational cost of newton multi-step method. the auxiliary function provides us the way to overcome the singul...

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t In this paper, we introduce a composite explicit viscosity iteration method of fixed point solutions of vari...

This paper addresses the consensus problem of nonlinear multiagent system with state constraints. A novel γ-type barrier Lyapunov function is adopted to handle with the bounded constraints. The iterative learning control strategy is introduced to estimate the unknown parameter and basic control signal. Five control schemes are designed, in turn, to address the consensus problem comprehensively ...

Prime factoring is important for multiple reasons. One is its central role in several cryptographic schemes. The central element of factoring is to find two prime numbers p, q where n = p ∗ q, given the value of n. A mathematical expression is developed that is amenable to iterative resolution of prime factors for a composite. The expression is then shown to admit a factoring process of P-compl...

In this paper the learnability of Iterative Learning Control (ILC) under the framework of energy function is explored. First we show that ILC is in essence a pointwise adaptation learning mechanism which can henceforth learn iterationindependent time-varying uncertainties. Next we propose a new robust ILC scheme to address norm-bounded uncertainties. The concept of Composite Energy Function (CE...

In this paper, we introduce the new concept of mutual Reich contraction that involves a pair operators acting on distance space. We chose framework strong b-metric spaces (generalizing standard metric spaces) in order to add more extended underlying structure. provide sufficient conditions for two mutually contractive maps have common fixed point. The result is family any cardinality. dynamics ...