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Shift-Invert Mode

Driver dndrv2  uses the shift-invert mode to find eigenvalues closest to a real shift This is often used to compute interior eigenvalues. For a discussion of shift-invert mode, see  3.2 in Chapter 3. To use dndrv2, the user is required to supply the action of

This is typically accomplished by factoring the matrix once before the iteration begins and then using this factorization repeatedly to solve the sequence of linear systems that arise during the calculation. The IRAM will find selected eigenvalues of depending on the setting of which. The recommended setting for computing the eigenvalues of A nearest to is which = 'LM'. If the desired shift has a nonzero imaginary part, then dndrv5 or dndrv6 should be modified to solve the problem. For eigenvalue problems where the additional storage needed is not prohibitive, the complex shift-invert driver zndrv2 should be used.

Chao Yang