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This paper is devoted to the computation of transmission eigenvalues in theinverse acoustic scattering theory. This problem is first reformulated as a twoby two boundary system of boundary integral equations. Next, utilizing theSchur complement technique, we develop a Schur complement operator withregularization to obtain a reduced system of boundary integral equations. TheNystr\"{o}m discretization is then used to obtain an eigenvalue problem for amatrix. We employ the recursive integral method for the numerical computationof the matrix eigenvalue. Numerical results show that the proposed method isefficient and reduces computational costs.

Computation of transmission eigenvalues by the regularized Schur complement for the boundary integral operators