HSL_MA79: Sparse symmetric system: mixed precision

HSL_MA79 is a mixed precision sparse symmetric solver for solving one or more linear systems \(\mathbf{AX} = \mathbf{B}\). A factorization of \(\mathbf{A}\) using single precision (that is, 32-bit real arithmetic) is performed using a direct solver (MA57 or HSL_MA77) and then refinement (iterative refinement and, in some cases, FGMRES) in double precision (that is, 64-bit real arithmetic) is used to recover higher accuracy. This technique is termed a mixed precision approach. If refinement fails to achieve the requested accuracy, a double precision factorization is performed.

Use of single precision arithmetic substantially reduces the amount of data that is moved around within a sparse direct solver, and on a number of modern architectures, it is currently significantly faster than double precision computation. Thus HSL_MA79 offers the potential of obtaining a solution to \(\mathbf{AX} = \mathbf{B}\) to double-precision accuracy more rapidly than using a direct solver in double precision. HSL_MA79 is primarily designed for solving very large systems.