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Subroutine `XYapps` applies the shifts using an implicitly
shifted QR
mechanism on the projected matrix If a shift is complex,
then `[s,d]napps` employs a double implicit shift application
so that the complex conjugate of the shift is applied simultaneously.
This allows the implicit shift application to take place
in real arithmetic. Finally, `XYapps` updates the current Arnoldi/Lanczos
basis to obtain the new length *k* factorization and Subdiagonal elements of the Hessenberg matrices are set to zero if they
satisfy the same criterion as used in a standard implementation of
the QR algorithm. (This amounts to checking if any subdiagonal
of is less than the product
of machine precision and the sum of the two adjacent diagonal elements of
)

*Chao Yang*

*11/7/1997*