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Complex tridiagonal skewhermitian eigensolver #56

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smataigne opened this issue Aug 16, 2022 · 2 comments
Closed

Complex tridiagonal skewhermitian eigensolver #56

smataigne opened this issue Aug 16, 2022 · 2 comments

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@smataigne
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Find a method to provide an eigensolver for SkewHermtridiagonal complex matrices
@smataigne
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smataigne commented Aug 16, 2022 •
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A SkewHermTridiagonal matrix can be transformed into a complex SymTridiagonal by unitary transformation but LAPACK provides no solver for complex symmetric tridiagonal matrices. Maybe implementing my own QR-algorithm would be worth since the matrix is already tridiagonal. It could certainly outperform hermitian eigensolvers.

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smataigne commented Aug 17, 2022 •
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SkewHermTridiagonal can be multiplied by $i$ to be turned into a Hermitian matrix. It can then be turned into real SymTridiagonal using "scalar " givens rotations. Then efficient solvers can be used. The orthogonal transformation will be diagonal, so very cheap to store and compute.

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