Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Improved automatic computation of Hessian matrix spectral bounds   This paper presents a fast and powerful method for the computation of
eigenvalue bounds for Hessian matrices $\nabla^2 \varphi(x) $ of nonlinear
functions $\varphi: U \subseteq R^n\rightarrow R$ on hyperrectangles $B \subset
U$. The method is based on a recently proposed procedure for an efficient
computation of spectral bounds using extended codelists. Both the previous
approach and the one presented here substantially differ from established
methods in that they do deliberately not use any interval matrices and thus
result in a favorable numerical complexity of order $O(n)\,N(\varphi)$, where
$N(\varphi)$ denotes the number of operations needed to evaluate $\varphi$ at a
point in its domain. We improve the previous method by exploiting sparsity,
which naturally arises in the underlying codelists.

23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex