arXiv subjects

Sanwar Ahmad

Publications and source records attributed to Sanwar Ahmad.

2 recordsLinked to original sources

arXiv2026

On Convergence of an Accelerated Modified Newton Method for Nonlinear Equations

Newton's iteration is a fundamental tool for root-finding and numerical solutions of systems of equations. The iteration rapidly refines the initial approximation to the exact root, and in general the convergence is quadratic. Since the method requires finding the function value and its derivative at each iteration, in some cases, it may not converge. This is because the value of the derivative gets close to zero. In this paper, we introduce a modified and stable algorithm of Newton's iteration method that addresses this issue, reduces computational cost, and improves efficiency. In addition. we analyze the convergence properties of the modified method to demonstrate its effectiveness.

math.NA↗

arXiv2020

Statistical Inversion Using Sparsity and Total Variation Prior And Monte Carlo Sampling Method For Diffuse Optical Tomography

In this paper, we formulate the reconstruction problem in diffuse optical tomography (DOT) in a statistical setting for determining the optical parameters, scattering and absorption, from boundary photon density measurements. A special kind of adaptive Metropolis algorithm for the reconstruction procedure using sparsity and total variation prior is presented. Finally, a simulation study of this technique with different regularization functions and its comparison to the deterministic Iteratively Regularized Gauss Newton method shows the effectiveness and stability of the method.

math.NA↗