Following the results of cite{Med}, regarding the Aluthge transform of polynomial matrices, the symbolic computation of the Duggal transform of a polynomial matrix $A$ is developed in this paper, using the polar decomposition and the singular value decomposition of $A$. Thereat, the polynomial singular value decomposition method is utilized, which is an iterative algorithm with numerical charac...

The changes in the nonnegative and positive polar factors of generalized polar decomposition and polar decomposition are studied under the additive perturbation. Some new perturbation bounds are obtained. These bounds are different from precious ones in form and measure and, in some cases, may be smaller than the corresponding existing ones. Furthermore, the corresponding perturbation bounds fo...

A quadratically convergent Newton method for computing the polar decomposition of a full-rank matrix is presented and analysed. Acceleration parameters are introduced so as to enhance the initial rate of convergence and it is shown how reliable estimates of the optimal parameters may be computed in practice. To add to the known best approximation property of the unitary polar factor, the Hermit...

Some new perturbation bounds of the positive (semi) definite polar factor and the (sub) unitary polar factor for the (generalized) polar decomposition under the general unitarily invariant norm and the spectral norm are presented. By applying our new bounds to the weighted cases, the known perturbation bounds for the weighted polar decomposition are improved. 2014 Elsevier Inc. All rights reser...

Abstract: It is shown that the polar decomposition theorem of operators in (real) Hilbert spaces gives rise to the known decomposition in boost and spatial rotation part of any matrix of the orthochronous proper Lorentz group SO(1, 3)↑. This result is not trivial because the polar decomposition theorem is referred to a positive defined scalar product while the Lorentz-group decomposition theore...

A new method is described for computing the singular value decomposition (SVD). It begins by computing the polar decomposition and then computes the spectral decomposition of the Hermitian polar factor. The method is particularly attractive for shared memory parallel computers with a relatively small number of processors, because the polar decomposition can be computed efficiently on such machi...