The project focuses on developing a new generation of numerical linear algebra algorithms that exploit current and future computers. Our algorithms will be fast and will be accompanied by rigorous error analysis to guarantee their reliability, even for the largest and most difficult problems. The target problems will be drawn from linear equations, linear least squares problems, eigenvalue problems, the singular value decomposition, and matrix function evaluation. These are the innermost kernels in many scientific and engineering applications---in particular, in data science and in machine learning---so it is essential that they are fast, accurate, and reliable.
A key aspect of this work is the exploitation of variable precision arithmetic. Low precision arithmetic is now available in hardware and is increasingly being used in machine learning and scientific computing more generally because of its speed, but its limited precision and narrow range require careful treatment. High precision (quadruple precision and above) is available in software and may be used in small amounts to speed up or stabilize an algorithm.
A strong background in numerical linear algebra and programming skills in MATLAB or a high level language are essential.