Research

Graduate Assistant, Department of Mathematics,
University of Florida, Gainesville, Florida, 32603
Aug 2018 – Present

  1. Deep Learning as an Optimal Control under the supervision of Dr. William Hager
    — Derived the back propagation algorithm of ANN and CNN using Lagrange Multiplier. 
     Compared the derived back propagation algorithm using Lagrange Multiplier with the standard back propagation derivation.

Research Associate, Department of Mathematical Sciences,
Cameron University, Lawton, Oklahoma, 73505
Jan 2016 – May 2018

  1.  Extending the Local Convergence Analysis of Newton’s Method under the supervision of Dr. Ioannis K. Argyros.
    Approximate a locally unique solution of a non- linear equation in a Banach Space setting.
    Developed and Implemented Computational Algorithm to compute the radius of convergence and error bounds.
  2. Comparing the Local Convergence Analysis of Some Newton-Like Methods for Solving Equations under the supervision of Dr. Ioannis K. Argyros.
    Compared the Analysis of Newton-Like Methods to approximate a locally unique solution of a non- linear equation in a Banach Space setting.
     
    Computed  the radii of convergence using two-step Newton Method and two-step Midpoint Method.
     Computed  the error bounds on the distances involved using Lipschitz constant.
  3. Mathematics behind a Guitar String under the supervision of Dr. Narayan Thapa.
    Studied the physics behind a guitar string.
     Analyzed the wave equation and solved IBVP.
     Interpreted the displacement function.