The speaker discusses the importance of sparse linear systems in technical and scientific computing and how these systems can be difficult to solve due to their size and numerical stability. The speaker presents a library they wrote, called Recursive Sparse Blocks (RSB), which respects the original Sparse BLAS API and provides building blocks for iterative solvers. RSB uses automated empirical optimization and is compatible with C++, Fortran, Octave, and Python. The library is licensed under LGPLv3 and is easily accessed through various packaged versions, including those from Debian Ubuntu and Windows. The speaker also suggests that the library can be used for multi-core and SciPy sparse operations.