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leburgel
added this pull request to stack #295
October 2, 2026 07:01
eig_trunc_pullback! iteration by the smallest eigenvalue and use _smith_iteration!
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Stacked on #287, which introduces a dedicated helper for the doubling-iteration Sylvester solve.
eig_trunc_pullback!still normalized its Sylvester iteration by the largest |eigenvalue|, somax|D̄⁻¹| = max|D| / min|D|can grow under repeated squaring and overflow when the retained eigenvalues span a large range. This is the same issue #282 fixed foreigh_trunc_pullback!.Changes:
max|D̄⁻¹|at 1 so squaring can only shrink it._smith_iteration!helper, as already done foreigh_trunc_pullback!andsvd_trunc_pullback!in Sum only one Neumann series insvd_trunc_pullback!#287.APᴴ = A' - ViG * (V * D)'directly rather thanAP, so the helper receives a plain matrix instead of anAdjoint, which avoids generic fallbacks on GPU.Behavioural note: as for
eigh_trunc_pullback!in #287, the first termAPᴴ X₀ D̄⁻¹is now also subject to thedegeneracy_atolstopping test instead of always being added.