Numerical stability in the calculation of eigenfrequencies using integral equations

摘要

We comment on a phenomenon of instability that appears while computing eigenfrequencies using the integral equation framework. More precisely, it is currently known that the real symmetric matrices are well, and sometimes the best, adapted to numerical treatment. However, we show that this is not the case, if we wish to determine with high accuracy the spectrum of elliptic, and other related operators, using integral representations.