Applied Mathematics Colloquium
Annenberg 105
Inverse Problems for Non-Self-Adjoint Operators
Mark Embree,
Professor,
Computational and Applied Mathematics,
Rice University,
Given a set of eigenvalues, can one accurately reconstruct a matrix or operator that produced them? When the eigenvalues are real and the operator is self-adjoint with fixed structure (Sturm-Liouville operators and their discretizations, Jacobi matrices), the answer is yes, and a variety of algorithms are available to effect the reconstruction.
Non-self-adjoint problems pose considerable practical and theoretical challenge, but are important for applications such as the design of damping for physical structures. Non-orthogonal eigenfunctions and consequent eigenvalue sensitivity complicate analysis, while damping can hamper eigenvalue measurement.
This talk will describe progress on two classes of inverse problems for non-self-adjoint operators: recovery of a viscous damping parameter in a vibrating string, and the inverse field of values problem for Rayleigh-Ritz eigenvalue estimates. The latter reveals that the Cauchy interlacing observed for Hermitian matrices has a natural analogue that holds even for non-diagonalizable matrices.
[Joint work with Russell Carden and Steve Cox]
Non-self-adjoint problems pose considerable practical and theoretical challenge, but are important for applications such as the design of damping for physical structures. Non-orthogonal eigenfunctions and consequent eigenvalue sensitivity complicate analysis, while damping can hamper eigenvalue measurement.
This talk will describe progress on two classes of inverse problems for non-self-adjoint operators: recovery of a viscous damping parameter in a vibrating string, and the inverse field of values problem for Rayleigh-Ritz eigenvalue estimates. The latter reveals that the Cauchy interlacing observed for Hermitian matrices has a natural analogue that holds even for non-diagonalizable matrices.
[Joint work with Russell Carden and Steve Cox]
For more information, please contact Sydney Garstang by phone at x4555 or by email at [email protected] or visit http://www.acm.caltech.edu.
Event Series
Applied Mathematics Colloquium Series