Using MultiPrecisonArrays.jl: Iterative Refinement in Julia
C. T. Kelley
TL;DR
This paper introduces MultiPrecisionArrays.jl, a Julia package for iterative refinement methods that enhances numerical accuracy, especially with future support for half precision in LAPACK/BLAS, currently focusing on double and single precision combinations.
Contribution
It presents a Julia package that implements various iterative refinement techniques, facilitating higher precision solutions in numerical linear algebra.
Findings
Supports classical iterative refinement with double precision equations and single precision factorizations
Provides data structures and solvers for multiple variants of iterative refinement
Anticipates improved utility with future half precision support in LAPACK/BLAS
Abstract
MultiPrecisionArrays.jl is a Julia package. This package provides data structures and solvers for several variants of iterative refinement. It will become much more useful when half precision (aka Float16) is fully supported in LAPACK/BLAS. For now, its only general-purpose application is classical iterative refinement with double precision equations and single precision factorizations.
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Taxonomy
TopicsModeling, Simulation, and Optimization · Mathematics, Computing, and Information Processing · Image Processing and 3D Reconstruction