How can we find the "best" matrix for a given task while meeting certain requirements? This question comes up in areas like engineering, finance, and statistics. For example, engineers might need to adjust a model to make a system stable, or financial analysts might need to estimate missing data in a correlation matrix. These challenges, called "matrix nearness problems", involve finding a matrix that is as close as possible to a starting one while obeying specific rules. Instead of relying on traditional methods, our project tackles these problems using a novel approach. We break the problem into two steps, one that can be solved exactly and one that involves optimising a function over a geometric structure. By combining cutting-edge mathematical techniques with efficient algorithms, we will solve matrix nearness problems faster and more accurately than ever before.

2025

2029