Block-oriented \(J\)-Jacobi methods for Hermitian matrices (Q710862)

The authors consider a method to accelerate the accurate eigensolver obtained by \textit{K. Veselić} [Numer. Math. 64, No.~2, 241--269 (1993; Zbl 0805.65038)]. This eigensolver applies to indefinite Hermitian matrices; the present authors transform it into a block-wise algorithm that can be implemented as a \texttt{BLAS 3} code. The authors prove the global convergence under block-oriented pivot strategies and they discuss the asymptotic converence. Numerical tests show that the block-oriented algorithm can be considerably faster than the non-block version, at least for large matrices. The paper is well-written with a good introduction and carefully given proofs of the important results.