Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the application of GMRES to oscillatory singular integral equations   We present a new method for the numerical solution of singular integral
equations on the real axis. The method's value stems from an explicit formula
for the Cauchy integral of a complex exponential multiplied by a rational
function. Additionally, the inner product of such functions is computed
explicitly. With these tools, the GMRES algorithm is applied to both
non-oscillatory and oscillatory singular integral equations. Ideas from
Fredholm theory and Riemann--Hilbert problems are used to motivate
preconditioners for these singular integral equations. A dramatic acceleration
in convergence is realized. This presents a strong link between the theory of
singular integral equations and the numerical analysis of such equations.
Furthermore, this method presents a first step towards a solver for the inverse
scattering transform that does not require the deformation of a
Riemann--Hilbert problem.

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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat