Linear Operator

Linear operators, fundamental mathematical objects mapping vectors or functions to others, are central to numerous scientific fields. Current research emphasizes efficient computation and representation of linear operators, particularly within large-scale applications like machine learning and solving partial differential equations. This includes developing novel algorithms leveraging quantum computing for speedup, designing efficient neural operator architectures (e.g., using multigrid methods), and exploring the use of multi-linear operators for reusing pretrained models. These advancements improve the scalability and efficiency of various computational tasks, impacting diverse areas from scientific computing to artificial intelligence.