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Efficient solution of the lowest eigenmodes is studied for a family ofrelated eigenvalue problems with common $2\times 2$ block structure. It isassumed that the upper diagonal block varies between different versions whilethe lower diagonal block and the range of the coupling blocks remainsunchanged. Such block structure naturally arises when studying the effect of asubsystem to the eigenmodes of the full system. The proposed method is based oninterpolation of the resolvent function after some of its singularities havebeen removed by a spectral projection. Singular value decomposition can be usedto further reduce the dimension of the computational problem. Error analysis ofthe method indicates exponential convergence with respect to the number ofinterpolation points. Theoretical results are illustrated by two numericalexamples related to finite element discretisation of the Laplace operator.

Efficient solution of symmetric eigenvalue problems from families of coupled systems