Block Preconditioned Harmonic Projection Method

A block preconditioned solver for large nonlinear eigenproblems

The BPHP method aims at computing a few eigenvalues of large nonlinear eigenproblems T(lambda)v = 0 around a specified shift sigma, using a proper preconditioner whose action on a vector u satisfies M^{-1}u \approx T(sigma)^{-1}u, without the need to solve the linear system T(sigma)x = u exactly. It is similar in spirit to LOBPCG and the Jacobi-Davidson method, but with more complex features to handle peculiarities of this type of eigenproblems.