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Try improve convergence dlaed4

Open weslleyspereira opened this issue 2 years ago • 0 comments

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.

weslleyspereira avatar Mar 15 '22 21:03 weslleyspereira