initial publication

.gitignore

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+*~
+*.jl.cov
+*.jl.*.cov
+*.jl.mem
+/deps/deps.jl
+/docs/build

.travis.yml

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+## Documentation: http://docs.travis-ci.com/user/languages/julia/
+language: julia
+os:
+  - linux
+  - osx
+julia:
+  - 1.0
+  - nightly
+notifications:
+  email: false
+git:
+  depth: 99999999
+
+## uncomment the following lines to allow failures on nightly julia
+## (tests will run but not make your overall status red)
+#matrix:
+#  allow_failures:
+#  - julia: nightly
+
+## uncomment following lines to deploy documentation
+# jobs:
+#   include:
+#     - stage: Documentation
+#       julia: 1.0
+#       os: linux
+#       script:
+#         - julia --project=docs -e 'using Pkg; Pkg.instantiate(); Pkg.develop(PackageSpec(path=pwd()))'
+#         - julia --project=docs --color=yes docs/make.jl
+#       after_success: skip
+after_success:
+  - julia --project=test/coverage -e 'using Pkg; Pkg.instantiate()'
+  - julia --project=test/coverage test/coverage/coverage.jl

LICENSE.md

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+The IterativeRefinement.jl package is licensed under the MIT "Expat" License:
+
+> Copyright (c) 2018: the IterativeRefinement.jl developers
+>
+> Permission is hereby granted, free of charge, to any person obtaining a copy
+> of this software and associated documentation files (the "Software"), to deal
+> in the Software without restriction, including without limitation the rights
+> to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+> copies of the Software, and to permit persons to whom the Software is
+> furnished to do so, subject to the following conditions:
+>
+> The above copyright notice and this permission notice shall be included in all
+> copies or substantial portions of the Software.
+>
+> THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+> IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+> FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+> AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+> LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+> OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+> SOFTWARE.
+>

README.md

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+# IterativeRefinement
+<!--
+![Lifecycle](https://img.shields.io/badge/lifecycle-experimental-orange.svg) -->
+![Lifecycle](https://img.shields.io/badge/lifecycle-maturing-blue.svg)<!--
+![Lifecycle](https://img.shields.io/badge/lifecycle-stable-green.svg)
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+[![Build Status](https://travis-ci.com/RalphAS/IterativeRefinement.jl.svg?branch=master)](https://travis-ci.com/RalphAS/IterativeRefinement.jl)
+[![codecov.io](http://codecov.io/github/RalphAS/IterativeRefinement.jl/coverage.svg?branch=master)](http://codecov.io/github/RalphAS/IterativeRefinement.jl?branch=master)
+
+This package is an implementation of multi-precision iterative refinement for
+linear matrix-vector problems of the form `A x = b`.
+
+# Basic Usage
+```julia
+julia> using LinearAlgebra, IterativeRefinement
+julia> x, bnorm, bcomp = rfldiv(A,b)
+```
+This provides an accurate solution vector `x` and estimated bounds
+onf norm-wise and component-wise relative error. By default `LU` decomposition
+is used.
+
+# Advanced Usage
+See the function docstring for details.
+
+If one has several right-hand-sides, one can equilibrate and factor
+`A` in advance; see the tests for an example.
+
+# Background
+The purpose of iterative refinement is to improve the accuracy of a
+solution.  If `x` is the exact solution, a simple solve of the form
+`y = A \ b` will have a relative forward error (`norm(y-x)/norm(x)`) of
+approximately `ϵ * O(n) * cond(A)` where `ϵ` is the unit roundoff error
+in the standard precision. Iterative refinement with higher precision
+residuals can reduce this to `ϵ * O(n)`, as long as the matrix `A` is
+not very badly conditioned relative to `ϵ`.
+
+Why not do everything in high precision? The factorization step is
+typically *much* more expensive in high precision, whereas the
+residual computation is relatively cheap. Furthermore, this scheme
+provides useful error bounds.
+
+For typical use, one would have a working precision of `Float64`
+(`ϵ = 2.2e-16`), so that fast LAPACK/BLAS routines dominate the runtime.
+`rfldiv` will then use `Double64` from
+[DoubleFloats.jl](https://github.com/JuliaMath/DoubleFloats.jl)
+for the residuals.
+
+# Reference
+To be precise, this package implements Algorithm 3 from J.Demmel et al.,
+"Error bounds from extra precise iterative refinement",
+LAPACK Working Note Nr. 165 (2005), also published as
+ACM TOMS, 32, 325 (2006).  The work
+described therein eventually turned into a collection of subroutines
+included in some versions of LAPACK.  This implementation is based on
+the paper; minor modifications were introduced based on experimentation.

REQUIRE

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+julia 0.7
+DoubleFloats 0.4