{d/s}laed2/8: Increase deflation tolerance to match {d/s}lasd2/7#1317
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{d/s}laed2/8: Increase deflation tolerance to match {d/s}lasd2/7#1317jschueller wants to merge 1 commit into
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The eigenvalue divide-and-conquer helper routines DLAED2/SLAED2 and DLAED8/SLAED8 used a deflation tolerance of 8*EPS, while the SVD routines DLASD2/SLASD2 and DLASD7/SLASD7 now use 64*EPS (since PR Reference-LAPACK#1286). The downstream eigenvector computation in DLAED3 divides by eigenvalue differences (DLAMBDA(I) - DLABMDA(J)), causing the same catastrophic cancellation when close eigenvalues escape deflation with the tighter tolerance. Raise all four routines to 64*EPS (EIGHT*EIGHT*EPS), matching the SVD path, so close eigenvalues are deflated and the eigenvector computation remains stable. Follow-up for Reference-LAPACK#255
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The eigenvalue divide-and-conquer helper routines DLAED2/SLAED2 and DLAED8/SLAED8 used a deflation tolerance of 8EPS, while the SVD routines DLASD2/SLASD2 and DLASD7/SLASD7 now use 64EPS (since PR #1286). The downstream eigenvector computation in DLAED3 divides by eigenvalue differences (DLAMBDA(I) - DLABMDA(J)), causing the same catastrophic cancellation when close eigenvalues escape deflation with the tighter tolerance.
Raise all four routines to 64EPS (EIGHTEIGHT*EPS), matching the SVD path, so close eigenvalues are deflated and the eigenvector computation remains stable.
Follow-up for #255
/cc @mgates3