Matrix Approximation

Matrix approximation aims to represent large matrices with smaller, computationally more manageable ones, preserving essential information while reducing storage and processing demands. Current research emphasizes efficient algorithms, such as those based on sketching techniques and iterative methods like Newton-Schulz, to achieve faster approximations for various matrix operations, including solving linear systems and computing matrix norms. These advancements are particularly impactful in fields like medical imaging and finance, where handling massive datasets is crucial, and also improve the efficiency of machine learning algorithms that rely heavily on matrix computations. Furthermore, research is actively exploring the development of differentially private algorithms for matrix approximation to protect sensitive data.