Eigenvalue optimisation problems involve identifying design or material configurations that either maximise or minimise the eigenvalues associated with differential operators under given boundary ...

Eigenvalue problems are fundamental to understanding the spectral characteristics of photonic and plasmonic systems. These problems involve determining the intrinsic resonant frequencies and modes of ...

This paper takes another look at the convergence analysis of the Arnoldi procedure for solving non-Hermitian eigenvalue problems. Two main viewpoints are put in contrast. The first exploits the ...

Taiwanese Journal of Mathematics, Vol. 26, No. 5 (October 2022), pp. 1045-1068 (24 pages) We consider how distribution of eigenvalues depends on boundary conditions of a discrete Laplacian operator on ...