This project concerns the development of computational methods in numerical linear algebra and their application to data-driven modelling in oceanography. The fundamental part of the project focuses on the development, analysis, and experimental evaluation of algorithms for large-scale matrix computations, including iterative methods and algorithms designed to exploit modern accelerator architectures. A second direction continues our work on computational oceanography, where numerical linear algebra and machine-learning methods are used for modelling and prediction from oceanographic data. The project will combine methodological research with computational experiments on both synthetic benchmark problems and real-world datasets. Research in this project is currently supported by SeRC.