Use of Refined Error Bound When Updating Eigenvalues of Tridiagonals

摘要

The Lanczos algorithm is used to compute some eigenvalues of a given symmetric matrix of large order. At each step of the Lanczos algorithm it is valuable to know which eigenvalues of the associated tridiagonal matrix have stabilized at eigenvalues of the given symmetric matrix. We present a robust algorithm which is fast (20j to 40j operation at j-th Lanczos step), uses about 30 words of extra storage, and has a fairly short program (approx 200 executable statements). (Author).