An accurate SVD algorithm for 2 by 2 triangular matrices

Using a fine accuracy analysis and the results from cite{har-mat-09}, a new accurate algorithm for computing the singular value decomposition of 2 by 2 triangular matrices is constructed. It is obtained by combining the new algorithm which is derived in cite{har-mat-09} and the algorithm which is coded as an xLASV2 computational routine of LAPACK. Relative error bounds for the output data of the hybrid algorithm are equal to or smaller than the same bounds for any of these two algorithms

Convergence of the Eberlein diagonalization method under the generalized serial pivot strategies

The Eberlein method is a Jacobi-type process for solving the eigenvalue problem of an arbitrary matrix. In each iteration two transformations are applied on the underlying matrix, a plane rotation and a non-unitary elementary transformation. The paper studies the method under the broad class of generalized serial pivot strategies. We prove the global convergence of the Eberlein method under the generalized serial pivot strategies with permutations and present several numerical examples.Comment: 16 pages, 3 figure