A minimal subspace residual method for large-scale eigenvalue problems

We present an iterative method for treating extremely large-scale eigenvalu e problems. Based on an exact formula and the GMRES method, our approach ge nerates a subspace which has the property that the residual of interior eig enpairs in the subspace is minimized. The result is that the corresponding large matrix is block-diagonalized iteratively. The accuracy of the final e igenpairs of interest is directly controlled by the accuracy of the GMRES p rocedure. Our method limits the number of Arnoldi iterations involved, and the dimension of the subspace, by including the residual in the subspace an d minimizing it at each step of the iteration. (C) 1999 American Institute of Physics. [S0021-9606(99)01516-0].