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Shift-Invert Mode

Driver dsdrv2  uses the shift-invert mode to find eigenvalues closest to a shift . This is often used to compute interior eigenvalues or clustered extremal eigenvalues. For a discussion of shift-invert mode, see  3.2 in Chapter 3. To use dsdrv2, 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 IRL iteration will find selected eigenvalues of depending on the setting of which. To compute the eigenvalues of ${\bf A}$ just to the right of , one should set which = 'LA' and for those just to the left set which = 'SA'. Eigenvalues closest to may be obtained by setting which = 'LM'. Eigenvalues to either side of may be obtained by setting which = 'BE'.

Chao Yang