An efficient method for computing eigenvalues of a real normal matrix
Journal of Parallel and Distributed Computing
Accelerating geoscience and engineering system simulations on graphics hardware
Computers & Geosciences
A Global Convergence Proof for Cyclic Jacobi Methods with Block Rotations
SIAM Journal on Matrix Analysis and Applications
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This paper presents new results concerning the effect of the ordering on the rate of convergence of the Jacobi iteration for computing eigenvalues of symmetric matrices. We start by showing that the diagonal elements converge for any ordering. Next we emphasize that different parts of the matrix converge at different speeds. Taking advantage of this phenomenon, we propose a strategy that leads to a convergence exponent of $ 3^{4/5} \approx 2.41$. Then we show that choosing the rotations to sort the diagonal can improve the convergence by a constant factor and we present experimental results on the performance of this new strategy.