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SUMMARY:Overcoming discretization issues for nonlinear eigenvalue problems
  using complex analysis and infinite-dimensional numerical linear algebra!
  - Matthew Colbrook (University of Cambridge)
DTSTART:20230726T103000Z
DTEND:20230726T113000Z
UID:TALK202798@talks.cam.ac.uk
DESCRIPTION:The first step when solving an infinite-dimensional eigenvalue
  problem is often to discretize it. However\, one must be extremely carefu
 l when discretizing nonlinear eigenvalue problems. Using examples\, we sho
 w that discretization can: (1) introduce spurious eigenvalues\, (2) entire
 ly miss spectra\, and (3) bring in severe ill-conditioning. While there ar
 e many eigensolvers for solving matrix nonlinear eigenvalue problems\, we 
 propose a solver for general holomorphic infinite-dimensional nonlinear ei
 genvalue problems that avoids discretization issues\, which we prove is st
 able and converges. Moreover\, we provide an algorithm that computes the p
 roblem's pseudospectra with explicit error control\, allowing verification
  of computed spectra. The algorithm and numerical examples are publicly av
 ailable in infNEP\, which is a software package written in MATLAB. Finally
 \, we show how this work fits into the bigger picture of recent progress i
 n the foundations of infinite-dimensional computations. This talk is based
  on joint work with&nbsp\;Alex Townsend (Cornell University).
LOCATION:Seminar Room 1\, Newton Institute
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