BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Transient dynamics under structured perturbations: bridging unstru
 ctured and structured pseudospectra - Christian Lubich
DTSTART:20250320T150000Z
DTEND:20250320T160000Z
UID:TALK229576@talks.cam.ac.uk
CONTACT:Matthew Colbrook
DESCRIPTION:As is known\, bounds of the resolvent of a matrix in the right
  complex half-plane yield bounds of solutions of homogeneous and inhomogen
 eous linear differential equations with this matrix. We ask two basic\nque
 stions:\n\n- Up to which size of structured perturbations are the resolven
 t norms of the perturbed matrices within a given bound in the right comple
 x half-plane?\n\n- For a given size of structured perturbations\, what is 
 the smallest common bound for the resolvent norms of the perturbed matrice
 s in the right complex half-plane?\n\nThis is considered for general linea
 r structures such as complex or real matrices with a given sparsity patter
 n or with restricted range and corange\, or special classes such as Toepli
 tz or Hankel matrices.\nConceptually\, we combine unstructured and structu
 red pseudospectra in a joint pseudospectrum\, allowing for the use of reso
 lvent bounds as with unstructured pseudospectra and for structured perturb
 ations as with structured pseudospectra. The above questions are addressed
  by an algorithm which solves eigenvalue optimization problems via suitabl
 y discretized rank-1 matrix differential equations. The talk is based on j
 oint work with Nicola Guglielmi.\n
LOCATION:Centre for Mathematical Sciences\, MR14
END:VEVENT
END:VCALENDAR