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update docstring
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src/interface/decompositions.jl

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@@ -116,20 +116,23 @@ See also [`DivideAndConquer`](@ref) and [`QRIteration`](@ref).
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@algdef SafeDivideAndConquer
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"""
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QRIteration(; [driver], fixgauge = default_fixgauge(), balanced = false)
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QRIteration(; [driver], fixgauge = default_fixgauge(), kwargs...)
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Algorithm type for computing the eigenvalue, Schur or singular value decomposition of a matrix via QR iteration.
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## Keyword arguments
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For non-Hermitian eigenvalue decomposition and Schur decomposition, the `balanced`
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keyword argument can be used to enable balancing of the matrix before the QR iteration,
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which can improve numerical accuracy for badly scaled matrices:
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- `balanced = false` (default): use the simple driver (`geev!`/`gees!`)
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- `balanced = true`: use the expert balanced driver (`geevx!`/`geesx!`)
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Various customizations are available, depending on the type of decomposition this algorithm is used for.
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For Schur decompositions, `expert = false` can be used to switch between `gees` and `geesx`.
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For non-Hermitian eigenvalue decompositions there is `permute = true` and `scale = true` to control whether
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or not to balance the input matrix before starting the QR iterations.
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For SVD and eigenvalue decompositions, there is residual freedom in the outputs that can be resolved.
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$_fixgauge_docs
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The optional `driver` keyword can be used to choose between different implementations of this algorithm.
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In all cases, the optional `driver` keyword can be used to choose between different implementations of this algorithm.
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"""
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@algdef QRIteration
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