Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence rate analysis and improved iterations for numerical radius
  computation   The main two algorithms for computing the numerical radius are the level-set
method of Mengi and Overton and the cutting-plane method of Uhlig. Via new
analyses, we explain why the cutting-plane approach is sometimes much faster or
much slower than the level-set one and then propose a new hybrid algorithm that
remains efficient in all cases. For matrices whose fields of values are a
circular disk centered at the origin, we show that the cost of Uhlig's method
blows up with respect to the desired relative accuracy. More generally, we also
analyze the local behavior of Uhlig's cutting procedure at outermost points in
the field of values, showing that it often has a fast Q-linear rate of
convergence and is Q-superlinear at corners. Finally, we identify and address
inefficiencies in both the level-set and cutting-plane approaches and propose
refined versions of these techniques.

4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics