Chapter 63
Structured Eigenvalue Problems — Structure-Preserving Algorithms, Structured Error Analysis
Heike Faßbender
Technische Universitat Braunschweig
Many eigenvalue problems arising in practice are structured due to (physical) properties induced by the original problem. Structure can also be introduced by discretization and linearization techniques. Preserving this structure can help preserve physically relevant symmetries in the eigenvalues of the matrix and may improve the accuracy and efficiency of an eigenvalue computation. This is well known for symmetric matrices A = AT ∈ ℝn×n. Every eigenvalue is real and every right eigenvector is also a left eigenvector belonging to the same eigenvalue. Many numerical methods, such as QR, Arnoldi, ...
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