Highly accurate symmetric eigenvalue decomposition and hyperbolic SVD
In the computation of eigenvalues and singular values, the relative accuracy may vary widely. Here the author sets out to analyse when it is possible to compute the hyperbolic singular value decomposition (SVD) with high relative accuracy. He shows that a one-sided hyperbolically orthogonal Jacobi method is well suited for this task. This in turn yields an algorithm which even for the normal symmetric eigenvalue problem has higher relative accuracy than the usual QR and Jacobi methods. This is demonstrated on some numerical examples.
scientific article; zbMATH DE number 1864806
scientific article