The rate of convergence of GMRES on a tridiagonal toeplitz linear system. II

This paper continues the recent work of the authors’ [R.-C. Li, W. Zhang, The rate of convergence of GMRES on a tridiagonal Toeplitz linear system, Numer. Math. 112 (2009) 267–293 (electronically published on 19 December 2008)] on the rate of convergence of GMRES for a tridiagonal Toeplitz linear system Ax=b. Much simpler formulas than the earlier ones for GMRES residuals when b is the first or the last column of the identity matrix are established, and these formulas allow us to confirm the rate of convergence that was conjectured but only partially proven earlier. Simpler and sharper bounds than earlier ones when all b’s entries, except its first and last ones, are zeros are also obtained.