Sanjeev Singh

Nitisha Aggarwal, Geetika Jain Saxena, Sanjeev Singh et al.

Generative AI techniques have opened the path for new generations of machines in diverse domains. These machines have various capabilities for example, they can produce images, generate answers or stories, and write codes based on the "prompts" only provided by users. These machines are considered 'thinking minds' because they have the ability to generate human-like responses. In this study, we have analyzed and explored the capabilities of artificial intelligence-enabled machines. We have revisited on Turing's concept of thinking machines and compared it with recent technological advancements. The objections and consequences of the thinking machines are also discussed in this study, along with available techniques to evaluate machines' cognitive capabilities. We have concluded that Turing Test is a critical aspect of evaluating machines' ability. However, there are other aspects of intelligence too, and AI machines exhibit most of these aspects.

Dhivya Prabhu K, Sanjeev Singh, Antony Vijesh

This paper develops an efficient iterative method for computing all zeros of solutions of second order ordinary differential equations. A third order Halleys method is first derived by approximating the solution of an associated Riccati differential equation. To improve computational efficiency, a modified Halleys method is proposed by fixing one of the functions in Halleys scheme as a constant. The modified Halleys method also retains third order convergence. Based on the behavior of the coefficients of the second order ODE, nonlocal convergence results are established for both Halleys and modified Halleys methods. Suitable initial guesses for computing all zeros of solutions of second order ODEs in a given interval are also presented for both methods. Furthermore, algorithms based on the modified Halleys method are developed for to compute all nodes and weights for Gauss Legendre and Gauss Hermite quadratures. A comparative numerical study with recent methods demonstrates the efficiency of the proposed algorithms.