Jacobi--Davidson Style QR and QZ Algorithms for the Reduction of Matrix Pencils
SIAM Journal on Scientific Computing
Large-Scale Computation of Pseudospectra Using ARPACK and Eigs
SIAM Journal on Scientific Computing
Solving Large-Scale Nonnormal Eigenproblems in the Aeronautical Industry Using Parallel BLAS
HPCN Europe 1994 Proceedings of the nternational Conference and Exhibition on High-Performance Computing and Networking Volume I: Applications
Gauss-Lobatto to Bernstein polynomials transformation
Journal of Computational and Applied Mathematics
High-Precision Numerical Simulations on a CUDA GPU: Kerr Black Hole Tails
Journal of Scientific Computing
Hi-index | 7.29 |
An efficient way of solving 2D stability problems in fluid mechanics is to use, after discretization of the equations that cast the problem in the form of a generalized eigenvalue problem, the incomplete Arnoldi-Chebyshev method. This method preserves the banded structure sparsity of matrices of the algebraic eigenvalue problem and thus decreases memory use and CPU time consumption. The errors that affect computed eigenvalues and eigenvectors are due to the truncation in the discretization and to finite precision in the computation of the discretized problem. In this paper we analyze those two errors and the interplay between them. We use as a test case the 2D eigenvalue problem yielded by the computation of inertial modes in a spherical shell. This problem contains many difficulties that make it a very good test case. It turns out that single modes (especially most-damped modes i.e. with high spatial frequency) can be very sensitive to roundoff errors, even when apparently good spectral convergence is achieved. The influence of roundoff errors is analyzed using the spectral portrait technique and by comparison of double precision and extended precision computations. Through the analysis we give practical recipes to control the truncation and roundoff errors on eigenvalues and eigenvectors.