Accurate ordering of eigenvectors and singular vectors without eigenvalues and singular values.
The author identifies a structural property of an eigenvector of a symmetric tridiagonal matrix which can be used to rank and ordering eigenvectors without knowing the eigenvalues. This is extended to singular vectors of bidiagonal matrices. These procedures do not require floating-point operations and hence are immune from round-off errors. The paper proposes a simple but powerful method for testing of computed eigensolutions and the singular value decomposition.
scientific article; zbMATH DE number 2005989