Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A communication-avoiding parallel algorithm for the symmetric eigenvalue
  problem   Many large-scale scientific computations require eigenvalue solvers in a
scaling regime where efficiency is limited by data movement. We introduce a
parallel algorithm for computing the eigenvalues of a dense symmetric matrix,
which performs asymptotically less communication than previously known
approaches. We provide analysis in the Bulk Synchronous Parallel (BSP) model
with additional consideration for communication between a local memory and
cache. Given sufficient memory to store $c$ copies of the symmetric matrix, our
algorithm requires $\Theta(\sqrt{c})$ less interprocessor communication than
previously known algorithms, for any $c\leq p^{1/3}$ when using $p$ processors.
The algorithm first reduces the dense symmetric matrix to a banded matrix with
the same eigenvalues. Subsequently, the algorithm employs successive reduction
to $O(\log p)$ thinner banded matrices. We employ two new parallel algorithms
that achieve lower communication costs for the full-to-band and band-to-band
reductions. Both of these algorithms leverage a novel QR factorization
algorithm for rectangular matrices.

30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg