A norm-reducing Jacobi-like algorithm for the eigenvalues of non-normal matrices

AbstractA new norm decreasing Jacobi-like method for reducing a non-normal matrix to a normal one is described. The method is an improved version of the Huang-Gregory's procedure [6], in which certain norm reducing non-optimal steps are replaced by the optimal ones, which correspond no more to regular matrix transformations. The method renders itself particularly effective in dealing with defective matrices of special forms. Theory and experiments alike indicate that this algorithm is in all computational aspects — accuracy, convergence rate, computing time, complexity of the computer program — better or at least as good as the original one.Both procedures, the original and the improved one, end in all of the authors computed examples with the diagonal matrix containing the eigenvalues of the non-normal initial matrix