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SUMMARY:What happens when you chop an equation? - Geoff Vasil (University 
 of Edinburgh)
DTSTART:20240201T150000Z
DTEND:20240201T160000Z
UID:TALK210124@talks.cam.ac.uk
CONTACT:Nicolas Boulle
DESCRIPTION:This talk will discuss a tricky business: truncating a differe
 ntial equation to produce finite solutions. A truncation scheme is often b
 uilt directly into the steps needed to create a numerical system. E.g.\, f
 inite differences replace exact differential operators with more manageabl
 e shadows\, sweeping the exact approach off the stage. \n\nIn contrast\, t
 his talk will discuss the "tau method" which adds an explicit parameterise
 d perturbation to an original equation. By design\, the correction calls i
 nto existence an exact (finite polynomial) solution to the updated analyti
 c system. The hope is that the correction comes out minuscule after compar
 ing it with a hypothetical exact solution. The tau method has worked splen
 didly in practice\, starting with Lanczos's original 1938 paper outlining 
 the philosophy. However\, why the scheme works so well (and when it fails)
  remains comparably obscure. While addressing the theory behind the Tau me
 thod\, this talk will answer at least one conceptual question: Where does 
 an infinite amount of spectrum go when transitioning from a continuous dif
 ferential equation to an exact finite matrix representation? 
LOCATION:Centre for Mathematical Sciences\, MR14
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