BEGIN:VCALENDAR
VERSION:2.0
PRODID:Linklings LLC
BEGIN:VTIMEZONE
TZID:Europe/Stockholm
X-LIC-LOCATION:Europe/Stockholm
BEGIN:DAYLIGHT
TZOFFSETFROM:+0100
TZOFFSETTO:+0200
TZNAME:CEST
DTSTART:19700308T020000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0200
TZOFFSETTO:+0100
TZNAME:CET
DTSTART:19701101T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTAMP:20210916T132451Z
LOCATION:Mère Royaume
DTSTART;TZID=Europe/Stockholm:20210707T143000
DTEND;TZID=Europe/Stockholm:20210707T150000
UID:submissions.pasc-conference.org_PASC21_sess155_msa307@linklings.com
SUMMARY:Mixed Precision s-step Lanczos and Conjugate Gradient Algorithms
DESCRIPTION:Minisymposium\n\nMixed Precision s-step Lanczos and Conjugate 
 Gradient Algorithms\n\nCarson\n\nCompared to the classical Lanczos algorit
 hm, the s-step Lanczos variant has the potential to improve performance by
  asymptotically decreasing the synchronization cost per iteration. However
 , this comes at a cost. Despite being mathematically equivalent, the s-ste
 p variant is known to behave quite differently in finite precision, with p
 otential for greater loss of accuracy and a decrease in the convergence ra
 te relative to the classical algorithm. It has previously been shown that 
 the errors that occur in the s-step version follow the same structure as t
 he errors in the classical algorithm, but with the addition of an amplific
 ation factor that depends on the square of the condition number of the O(s
 )-dimensional Krylov bases computed in each outer loop. As the condition n
 umber of these s-step bases grows (in some cases very quickly) with s, thi
 s limits the parameter s that can be chosen and thus limits the performanc
 e that can be achieved. In this work we show that if a select few computat
 ions in s-step Lanczos are performed in double the working precision, the 
 error terms then depend only linearly on the conditioning of the s-step ba
 ses. This has the potential for drastically improving the numerical behavi
 or of the algorithm with little impact on per-iteration performance. Our n
 umerical experiments demonstrate the improved numerical behavior possible 
 with the mixed precision approach, and also show that this improved behavi
 or extends to the s-step CG algorithm in mixed precision.\n\nDomain: CS an
 d Math
END:VEVENT
END:VCALENDAR