Global and quadratic convergence of the block Jacobi method for Hermitian matrices under the de Rijk pivot strategy
Vjeran Hari · ETNA - Electronic Transactions on Numerical Analysis · 2025
This paper provides a proof of global and quadratic convergence of the block Jacobi method for Hermitian matrices under the de Rijk pivot strategy. Also global and quadratic convergence of the element-wise Jacobi method under the same pivot strategy is proved. It is shown that sharp quadratic convergence bounds can be deduced from an estimate that is obtained in the global convergence proof. Numerical tests illustrate the behavior of the methods under the de Rijk pivot strategy.