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Try improve convergence dlaed4
Description, and suggested fix from Professor Ren-Cang Li, University of Texas at Arlington
Consider the case of computing the last updated eigenvalue using DLAED4
. If C=0
, ETA
is currently set to
DLTUB (upper bound) - TAU
Chances exist that TAU
is close to the desired value DLAM - D(N)
. In such a case, the current initial guess for ETA
would be very close to the upper bound (either RHO
or RHO/2
). As a result, it may take a lot more iterations to get to DLAM - D(N)
eventually.
One idea is to use a Newton step instead, i.e.,
ETA = -W / ( DPSI+DPHI )
This is the same initial step adopted when W*ETA.GT.ZERO
.