We compare five implementations of the Jacobi method for diagonalizing a symmetric matrix. Two of these, the classical Jacobi and sequential sweep Jacobi, have been used on sequential processors. The third method, the parallel sweep Jacobi, has been proposed as the method of choice for parallel ...
at hand, h can be represented as a block matrix $$\begin{aligned} h=\begin{bmatrix} \pi _{\mathcal {l}} (-\delta _2+v_l)\pi _{\mathcal {l}} & \quad \pi _{\mathcal {l}} v_l\pi _{\mathcal {h}} \\ \pi _{\mathcal {h}} v_l\pi _{\mathcal {l}} & \...
A direct parallel algorithm to tridiagonalize a real symmetric matric matrix using Givens transformation is presented. The algorithm is optimal and has a time complexity of O(NlogN) for matrices of order N.doi:10.1080/10637199408915424RAJASETHUPATHY, K. S....
This report describes an error analysis of Kaiser's algorithm for diagonalizing a real symmetric matrix. Use of the Kaiser algorithm to produce an eigenvalue is compared timewise with the Householder-Ortega algorithm. The divergence of maximal bounds for iterative processes from the actual cumulative...
In this paper, we consider a generalization of Ebenbauer's differential equation for non-symmetric matrix diagonalization to a flow on arbitrary complex semisimple Lie algebras. The flow is designed in such a way that the desired diagonalizations are precisely the equilibrium points in a given ...