Conjugate gradient-boundary element solution to the Cauchy problem for Helmholtz-type equations
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In this paper, an iterative algorithm based on the conjugate gradient method (CGM) in combination with the boundary element method (BEM) for obtaining stable approximate solutions to the Cauchy problem for Helmholtz-type equations is analysed. An efficient regularising stopping criterion for CGM proposed by Nemirovskii  is employed. The numerical results obtained confirm that the CGM + BEM produces a convergent and stable numerical solution with respect to increasing the number of boundary elements and decreasing the amount of noise added into the input data.
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