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SUMMARY:Pseudospectral Shattering and Diagonalization in Nearly Matrix Mul
 tiplication Time
DTSTART:20210401T161500
DTEND:20210401T171500
DTSTAMP:20260412T070954Z
UID:53247b371562c636a2b6ba7d3b46418b325eb36e7e867c0e56970e7c
CATEGORIES:Conferences - Seminars
DESCRIPTION:Professor Nikhil Srivastava (UC Berkeley)\nWe give an algorith
 m which diagonalizes an n x n complex matrix up to backward error delta 
 in O(n^{\\omega+o(1)}polylog(n/delta))\nbit operations  in finite arithme
 tic with O(polylog(n/delta)) bits of precision\, substantially improving t
 he previously known running time of O(n^10/delta^2). The two key ingredien
 ts are (1) A random matrix theory result showing that every matrix is clos
 e to one with well-conditioned eigenvalues and eigenvectors\, resolving a 
 conjecture of E.B. Davies. (2) A rigorous analysis of Roberts' Newton iter
 ation method for computing the matrix sign function in finite arithmetic\,
  itself an open problem in numerical analysis since the 80's.\n\nJoint w
 ork with J. Banks\, J. Garza-Vargas\, A. Kulkarni\, and S. Mukherjee.\n 
LOCATION:https://epfl.zoom.us/j/86801773416
STATUS:CONFIRMED
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