RLinearAlgebra

RLinearAlgebra is a Julia library for the development and application of randomized algorithms to the problems of forming low rank approximations to matrices and finding the solution of linear systems and least squares problems. Because of the large diversity of randomized techniques, rather than offering isolated routine implementations of algorithms, this library implements a series of extendable data structures and methods which allow code reuse.

Documentation structure

This documentation serves both as a manual to the library and as an introduction to randomized linear approximation techniques and randomized linear algebra solvers. We divide it in four parts:

• Tutorial: examples of how to solve linear systems and least squares problems with RLinearAlgebra and how to extend the library.
• Manual: here we offer an introduction to solving linear systems with randomized linear algebra techniques, compressing a matrix, and forming a low-rank approximation of a matrix. We introduce theoretical foundations and we provide code examples with RLinearAlgebra.
• API: a detailed description of all the data structures and methods of the library.
• Development: detailed instructions on how to contribute to the library.

Acknowledgements

This work is supported by the National Science Foundation Office of Advanced Cyberinfrastructure under awards 2309445 and 2309446. This material is based upon work supported by the U.S. Department of Energy, Office of Science, under contract number DE-AC02-06CH11357.