On the Parallel Implementation of Jacobi and Kogbetliantz Algorithms

Modified Jacobi and Kogbetliantz algorithms are derived by combining methods for modifying the orthogonal rotations. These methods are characterized by the use of approximate orthogonal rotations and the factorization of these rotations. The presented new approximations exhibit better properties and require less computational cost than known approximations. Suitable approximations are applied together with factorized rotation schemes in order to gain square root free or square root and division free algorithms. The resulting approximate and factorized rotation schemes are highly suited for parallel implementations. The convergence of the algorithms is analyzed and an application in signal processing is discussed.