There is a growing demand for and availability of multiprecision arithmetic: floating point arithmetic supporting multiple, possibly arbitrary, precisions. Demand in applications includes both high precision (long-term simulations and solving very ill conditioned problems) and low precision (climate modelling and deep learning). We discuss
- The need for, availability of, and ways to exploit, higher precision arithmetic (e.g., quadruple precision arithmetic).
- How to derive linear algebra algorithms that will run in any precision, as opposed to be being optimized (as some key algorithms are) for double precision.
- For solving linear systems with the use of iterative refinement, the benefits of suitably combining three different precisions of arithmetic (say, half, single, and double).
- How a new form of preconditioned iterative refinement can be used to solve very ill conditioned sparse linear systems to high accuracy.