We describe how variable precision floating point arithmetic can be used in the iterative solver GMRES. We show how the precision of the inner products carried out in the algorithm can be reduced as the iterations proceed, without affecting the convergence rate or final accuracy achieved by the iterates. Our analysis explicitly takes into account the resulting loss of orthogonality in the Arnoldi vectors. We also show how inexact matrix-vector products can be incorporated into this setting.
abstract = "We describe how variable precision floating point arithmetic can be used inthe iterative solver GMRES. We show how the precision of the inner productscarried out in the algorithm can be reduced as the iterations proceed, withoutaffecting the convergence rate or final accuracy achieved by the iterates.Our analysis explicitly takes into account the resulting loss of orthogonalityin the Arnoldi vectors. We also show how inexact matrix-vector products canbe incorporated into this setting.",
N2 - We describe how variable precision floating point arithmetic can be used inthe iterative solver GMRES. We show how the precision of the inner productscarried out in the algorithm can be reduced as the iterations proceed, withoutaffecting the convergence rate or final accuracy achieved by the iterates.Our analysis explicitly takes into account the resulting loss of orthogonalityin the Arnoldi vectors. We also show how inexact matrix-vector products canbe incorporated into this setting.
AB - We describe how variable precision floating point arithmetic can be used inthe iterative solver GMRES. We show how the precision of the inner productscarried out in the algorithm can be reduced as the iterations proceed, withoutaffecting the convergence rate or final accuracy achieved by the iterates.Our analysis explicitly takes into account the resulting loss of orthogonalityin the Arnoldi vectors. We also show how inexact matrix-vector products canbe incorporated into this setting.