Yao Zhang - Computing

Scientific computing is an interdisciplinary field that employs numerical methods and computational technologies to address complex scientific problems. It consists of three core components: numerical linear algebra, numerical optimization, and numerical solutions of differential equations.

Numerical linear algebra focuses on solving matrix and vector problems, such as linear equations and eigenvalue problems. This area provides essential tools for various applications in science and engineering, particularly when dealing with large, sparse matrices. Building on this foundation, numerical optimization seeks to find the optimal solution for functions, with or without constraints. This component is crucial in fields like machine learning and data analysis, where optimization techniques are instrumental in model training and decision-making.

Numerical solutions of differential equations involve solving ordinary and partial differential equations using techniques like finite difference, finite element, and finite volume methods. These approaches are vital for modeling physical phenomena, especially in fluid dynamics and heat transfer. Together, these components form the backbone of scientific computing, enabling the simulation and resolution of complex real-world problems across various disciplines.