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Regular Inverse Mode

  Driver dsdrv3  uses the regular inverse mode to solve the generalized eigenvalue problem. This mode is appropriate when ${\bf M}$ is symmetric and positive definite but it is not feasible to compute a sparse direct Cholesky factorization . It might also be appropriate if ${\bf M}$ can be factored but there is reason to think that ${\bf M}$ is ill-conditioned. To use dsdrv3 the user must supply the action of

The action of is typically done with an iterative solver such as pre-conditioned conjugate gradient. The use of ${\bf M}$-inner products restores symmetry. If ${\bf M}$ can be factored and is reasonably well conditioned, then direct conversion to a standard problem is recommended. Also, note that if A is positive definite and the smallest eigenvalues are sought, then it is best to reverse the roles of ${\bf A}$ and ${\bf M}$ and compute the largest eigevalues of . The reciprocals of these will then be the eigenvalues of interest.

Chao Yang