Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence and round-off errors in a two-dimensional eigenvalue problem
  using spectral methods and Arnoldi-Chebyshev algorithm   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 two-dimensional 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 that single modes (especially most-damped modes i.e. with high spatial
frequency) can be very sensitive to round-off errors, even when apparently good
spectral convergence is achieved. The influence of round-off 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 round-off errors on eigenvalues and eigenvectors.

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The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
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The categories of this paper are: eess
27
The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ