FACTORED ORTHOGONAL TRANSFORMATIONS FOR RECURSIVE EIGENDECOMPOSITION

Factorizations of orthogonal matrices play an important role in modern digital signal processing. Here we focus on their usefulness in the f ield of recursive eigendecomposition methods. We concentrate on recurs ive algorithms which use Givens rotations to update the eigenvector ma trix. The orthogonality of the estimated eigenvector matrix is known t o be crucial for the numerical stability of the recursive algorithms. It is shown that this property can be enforced by decomposing the orth ogonal matrix into a sequence of simple plane rotations. Then a rotati on method for updating the plane rotations is developed. This method h as the advantage that loss of numerical accuracy is avoided while reta ining the inherent parallel structure of the algorithm. Moreover, it c onsists solely of rotation operations. Therefore, the new method is id eally suited for execution on parallel architectures which have dedica ted rotation nodes, such as a CORDIC processor.