Nonlinear systems arise naturally in many areas of mathematics, engineering, and the physical sciences. My research in this area focuses on the development, analysis, and implementation of Broyden-like methods and other iterative techniques for solving high-dimensional nonlinear systems efficiently and reliably.
Research Topics
• Broyden-like Methods
• Quasi-Newton Methods
• Iterative Methods for Nonlinear Systems
• Large-Scale Nonlinear Systems
• Numerical Solution of Nonlinear Equations
• Convergence Analysis of Iterative Algorithms
Research Contributions
• Development of robust Broyden-like algorithms for systems of nonlinear equations
• Construction and analysis of quadrature-based Broyden-like methods
• Investigation of convergence properties of iterative methods
• Efficient numerical techniques for high-dimensional nonlinear systems
• Applications of nonlinear solvers in scientific computing
Selected Publications
• Quadrature Based Broyden-like Method for Systems of Nonlinear Equations (2018)
• Construction of a Broyden-like Method for Nonlinear Systems of Equations (2017)
• Robust Three-Step Broyden-like Algorithms for Functions of Several Variables
• A Robust Broyden-like Method for Systems of Nonlinear Equations (2018)
Research Goal
To develop efficient, robust, and reliable iterative algorithms for solving large-scale nonlinear systems arising in mathematics, engineering, and scientific computing. This research has resulted in several peer-reviewed publications on Broyden-like methods, quasi-Newton techniques, and numerical algorithms for high-dimensional nonlinear systems.