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An Efficient Jacobi-Like Algorithm for Parallel Eigenvalue Computation
September 1993 (vol. 42 no. 9)
pp. 1058-1065

A very fast Jacobi-like algorithm for the parallel solution of symmetric eigenvalue problems is proposed. It becomes possible by not focusing on the realization of the Jacobi rotation with a CORDIC processor, but by applying approximate rotations and adjusting them to single steps of the CORDIC algorithm, i.e., only one angle of the CORDIC angle sequence defines the Jacobi rotation in each step. This angle can be determined by some shift, add and compare operations. Although only linear convergence is obtained for the most simple version of the new algorithm, the overall operation count (shifts and adds) decreases dramatically. A slow increase of the number of involved CORDIC angles during the runtime retains quadratic convergence.

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Index Terms:
Jacobi-like algorithm; parallel eigenvalue computation; symmetric eigenvalue problems; CORDIC processor; CORDIC angle sequence; Jacobi rotation; linear convergence; quadratic convergence; approximate rotations; digital signal processing; eigenvalue computation; fast implementations; matrix computation; scaling computation; convergence of numerical methods; eigenvalues and eigenfunctions; matrix algebra; parallel algorithms; signal processing.
J. Gotze, S. Paul, M. Sauer, "An Efficient Jacobi-Like Algorithm for Parallel Eigenvalue Computation," IEEE Transactions on Computers, vol. 42, no. 9, pp. 1058-1065, Sept. 1993, doi:10.1109/12.241595
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