Abstract
A fast method for enclosing each eigenpairs of real symmetric matrix is proposed. First, error bounds of all approximate eigenvectors are proposed. The proposed method is constructed by combining these bounds and the fast method for enclosing each eigenvalue previously developed by the authors. Utilizing intermediate results in the previous method, computational cost for enclosing each eigenvector become almost negligible. Numerical results are presented showing the efficiency of the proposed method. As an application of the proposed method, an efficient method of bounding each pair of singular value and singular vector of a real matrix is sketched.
