A real triple dqds algorithm for the nonsymmetric tridiagonal eigenvalue problem

The paper discusses the following topics: attractions of the real tridiagonal case, relative eigenvalue condition number for matrices in factored form, dqds, triple dqds, error analysis, new criteria for splitting and deflation, eigenvectors of the balanced form, twisted factorizations and generalized Rayleigh quotient iteration. We present our fast real arithmetic algorithm and compare it with alternative published approaches.FCT -Fundação para a Ciência e a Tecnologia(UIDB/00013/2020