An efficient D-N alternating algorithm for solving an inverse problem for Helmholtz equation

<p style='text-indent:20px;'>Data completion known as Cauchy problem is one most investigated inverse problems. In this work we consider a associated with Helmholtz equation. Our concerned the convergence of well-known alternating iterative method [<xref ref-type="bibr" rid="b25">25</xref>]. main result to restore for classical algorithm (KMF) when wave numbers are considerable. This achieved by, some simple modification Neumann condition on under-specified boundary and replacement by relaxed ones. Moreover, small number <inline-formula><tex-math id="M111111">\begin{document}$ k $\end{document}</tex-math></inline-formula>, KMF algorithm's rid="b25">25</xref>] ensured, our can be used an acceleration convergence.</p><p style='text-indent:20px;'>In case, present theoretical results algorithm. Meanwhile it, deduce intervals related relaxation parameters in different situations. contrast existing results, proposed implement converges all choice number.</p><p style='text-indent:20px;'>We approach using finite element obtain accurate numerical affirm prove it's effectiveness.</p>