A fast algorithm for calculating the parameters for Jacobi rotations with reduced hardware requirements

Due to the permantly increasing computing power eigenvalue decompositions in real time embedded systems become more and more feasible. Applying a series of orthogonal similarity transforms, so called Jacobi rotations, provides one approach of solving the symmetric eigenvalue problem. Jacobi rotations are suitable for hardware implementation because of their regularity and their inherent parallelism. However, the calculation of the rotation parameters requires numerical operations which increase the hardware effort and processing time dramatically. We propose a new algorithm with considerably less hardware requirements but still having good numerically properties. Our new algorithm only needs one division with reduced precision and a small look-up table. Square roots, further divisions and other operations all with full precision are now unnecessary. Especially in highly parallel systems like systolic arrays a considerable amount of calculation time can be saved while decreasing the hardware effort.