Shift-Invert Mode

  Driver dsdrv4  uses the shift-inverse mode to solve the generalized eigenvalue problem. Eigenvalues closest to a shift can be obtained by computing selected eigenvalues for

To compute the eigenvalues of () 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 = 'BE'.

The eigenvalue of the original problem and are related by

To use dsdrv4, the user is required to supply the two matrix vector operations

where is the shift defined by the user. Typically, the above matrix operation is performed by factoring once at the beginning and and then using this factorization repeatedly to solve the resulting linear system. Note, this will require a symmetric indefinite factorization whenever is a point in the interior of the spectrum of (). A general (sparse) LU factorization may also be used, but there will be a storage penalty for ignoring symmetry.