Quadratic convergence of scaled matrices in Jacobi method

Summary. A quadratic convergence bound for scaled Jacobi iterates is proved provided the initial symmetric positive definite matrix has simple eigenvalues. The bound is expressed in terms of the off-norm of the scaled initial matrix and the minimum relative gap in the spectrum. The obtained result can be used to predict the stopping moment in the two-sided and especially in the one-sided Jacobi method. Received October 31, 1997 / Revised version received March 8, 1999 / Published online July 12, 2000