The new NAG® Library Mark 27. 3 ‘FEAST’ Eigensolver is particularly useful for techniques such as modelling the oscillations of railway tracks, or the simulation of fluid flows and electronic structure computations for example. Developed by Professor Eric Polizzi (and collaborators), FEAST Eigenvalue Solver works in a completely different way from other eigensolvers and, as a result, has some very useful properties in that it:

• Searches only eigenvalues lying within a user-specified contour in the complex plane.
• Can be used to solve standard, generalized and polynomial eigenvalue problems.
• Is available for complex, real, symmetric, Hermitian, and non-symmetric problems.
• Can be used for both large, sparse and small, dense problems.

It is the first property that really differentiates FEAST from other eigensolvers. This is particularly useful when applied to large, sparse eigenproblems when a subset of the spectrum is required. Solvers such as ARPACK are typically only able to find the largest/smallest magnitude eigenvalues or a specified number of eigenvalues close to a given complex value. Only the FEAST eigensolver can search within a specific contour within which the number of eigenvalues might be unknown.