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Subroutine [s,d]Yconv  declares that a Ritz value is an acceptable approximation to an eigenvalue of OP if is satisfied where is machine precision.   Subroutine [c,z]naup2  performs the checks directly within the code. The value of tol is defined by the user and has a default of machine precision .Since ARPACK avoids computation of the direct residual when assessing the numerical quality of the Ritz pair.

CAUTION: Only for symmetric (Hermitian) eigenproblems may the user assume that a computed Ritz value is an accurate approximation to an eigenvalue of OP. As § 4.6 of Chapter 4 explained, determining whether an IRAM computes accurate eigenvalues for non-symmetric (non Hermitian) eigenproblems depends on the sensitivity of the eigenproblem. If OP arises from a shift-invert spectral transformation, then the eigenvector purification step performed by XYeupd will most likely result in smaller residuals for the original problem than those obtained for OP (See (4.5.1) in Chapter 4).

Chao Yang