Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Subspace acceleration for large-scale parameter-dependent Hermitian
  eigenproblems   This work is concerned with approximating the smallest eigenvalue of a
parameter-dependent Hermitian matrix $A(\mu)$ for many parameter values $\mu
\in \mathbb{R}^P$. The design of reliable and efficient algorithms for
addressing this task is of importance in a variety of applications. Most
notably, it plays a crucial role in estimating the error of reduced basis
methods for parametrized partial differential equations. The current
state-of-the-art approach, the so called Successive Constraint Method (SCM),
addresses affine linear parameter dependencies by combining sampled Rayleigh
quotients with linear programming techniques. In this work, we propose a
subspace approach that additionally incorporates the sampled eigenvectors of
$A(\mu)$ and implicitly exploits their smoothness properties. Like SCM, our
approach results in rigorous lower and upper bounds for the smallest
eigenvalues on $D$. Theoretical and experimental evidence is given to
demonstrate that our approach represents a significant improvement over SCM in
the sense that the bounds are often much tighter, at negligible additional
cost.

32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org