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Driver dsdrv6 implements the Cayley spectral
transformation. Eigenvalues closest to a shift
can be obtained by computing the selected eigenvalues
Settings of which are the same as those of the shift-invert modes.
It is easy to verify that OP is symmetric with respect
to the (semi) inner product defined by so it is best to
use -inner products with this transformation.
The eigenvalue of the original problem and are
Note that the transformation becomes ill-defined as since . The expression does have a
limit as but it would be better to use
regular inverse mode or to use shift-invert mode with when eigenvalues near the origin are sought.
The Cayley transformation has slightly different properties than the
standard shift and invert
spectral transformation used by drivers dsdrv3 and dsdrv4.
To use this driver, the operations