A twisted factorization method for complex symmetric tridiagonal eigenvalue decomposition

We present a twisted factorization algorithm for computing the eigenvectors of an n-by-n nondefective irreducible complex symmetric tridiagonal matrix, given computed eigenvalues. Our algorithm requires 0(n ² ) flops for all the eigenvectors when the multiplicities of the eigenvalues are not large. Since all the eigenvalues of a complex symmetric tridiagonal matrix can be computed in 0(n ²) flops, our algorithm leads to a complete eigenvalue …