Igor Schein on Mon, 08 Dec 2003 07:10:39 +0100


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zetak()/zetakinit() numeric instability 

Hi,

? \p28
   realprecision = 28 significant digits
? zetak(zetakinit(t),3-1e-28)
1.202056914001922028212736502			\\ stable
? \p38
   realprecision = 38 significant digits
? zetak(zetakinit(t),3-1e-38)
304501015214.86169193987493921482289261		\\ unstable
? \p48
   realprecision = 48 significant digits
? zetak(zetakinit(t),3-1e-48)
304501015214.861691940846662404647333776169774851	\\ still unstable	
? \p57
   realprecision = 57 significant digits
? zetak(zetakinit(t),3-1e-57)
1.20109594617617987320510241163736976045912741685151078781	\\ back to stable

OTOH, zeta() is stable throughout.

Thanks

Igor