Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computing the smallest eigenvalue of large ill-conditioned Hankel
  matrices   This paper presents a parallel algorithm for finding the smallest eigenvalue
of a particular form of ill-conditioned Hankel matrix, which requires the use
of extremely high precision arithmetic. Surprisingly, we find that
commonly-used approaches that are designed for high efficiency are actually
less efficient than a direct approach under these conditions. We then develop a
parallel implementation of the algorithm that takes into account the unusually
high cost of individual arithmetic operations. Our approach combines message
passing and shared memory, achieving near-perfect scalability and high
tolerance for network latency. We are thus able to find solutions for much
larger matrices than has been previously possible, with the potential for
extending this work to systems with greater levels of parallelism.

16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys