Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximating linear response by nonintrusive shadowing algorithms   Nonintrusive shadowing algorithms efficiently compute $v$, the difference
between shadowing trajectories, then use $v$ to compute derivatives of averaged
objectives of chaos with respect to parameters of the dynamical system.
However, previous proofs of shadowing methods wrongly assume that shadowing
trajectories are representative. In contrast, the linear response formula is
proved rigorously, but is more difficult to compute.
  We prove that $v$ gives only a part, called the shadowing contribution, of
the linear response; hence, the other part, the unstable contribution, is the
systematic error of shadowing methods. For systems with a small ratio of
unstable dimensions, with some further statistical assumptions, we show that
the unstable contribution is small. We also briefly describe an algorithm for
the unstable contribution, which is simpler to derive but less efficient than
the fast linear response algorithm.
  Moreover, we prove the convergence of the nonintrusive shadowing algorithm,
the fastest shadowing algorithm, to $v$ and to the shadowing contribution.

13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol