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The FEAST eigenvalue algorithm is a subspace iteration algorithm that usescontour integration in the complex plane to obtain the eigenvectors of a matrixfor the eigenvalues that are located in any user-defined search interval. Bycomputing small numbers of eigenvalues in specific regions of the complexplane, FEAST is able to naturally parallelize the solution of eigenvalueproblems by solving for multiple eigenpairs simultaneously. The traditionalFEAST algorithm is implemented by directly solving collections of shiftedlinear systems of equations; in this paper, we describe a variation of theFEAST algorithm that uses iterative Krylov subspace algorithms for solving theshifted linear systems inexactly. We show that this iterative FEAST algorithm(which we call IFEAST) is mathematically equivalent to a block Krylov subspacemethod for solving eigenvalue problems. By using Krylov subspaces indirectlythrough solving shifted linear systems, rather than directly for projecting theeigenvalue problem, IFEAST is able to solve eigenvalue problems using verylarge dimension Krylov subspaces, without ever having to store a basis forthose subspaces. IFEAST thus combines the flexibility and power of Krylovmethods, requiring only matrix-vector multiplication for solving eigenvalueproblems, with the natural parallelism of the traditional FEAST algorithm. Wediscuss the relationship between IFEAST and more traditional Krylov methods,and provide numerical examples illustrating its behavior.

An improved Krylov eigenvalue strategy using the FEAST algorithm with inexact system solves