Precision of AiryAi[0.0]
- To: mathgroup at smc.vnet.net
- Subject: [mg103466] Precision of AiryAi[0.0]
- From: Mark McClure <mcmcclur at unca.edu>
- Date: Wed, 23 Sep 2009 07:25:11 -0400 (EDT)
Running V7.0.1 on my 64 bit MacBook Pro. The result of the simple computation AiryAi[0.0] returns a result with a precision of 15.9, rather than the expected MachinePrecision. That is, we get: Precision[AiryAi[0.0]] 15.9546 Rather than MachinePrecision as in Precision[BesselJ[2, 0.0]] MachinePrecision Does anyone have an explanation for this? This occurs with all of the Airy related functions, but none of the other special functions I've tried have this strange behavior. Of course, some computations (like 2^2000.0) can lead to arbitrary precision results, simply because the result can't be expressed in IEEE floating point arithmetic. AiryAi[0.0] is about 0.355, however, so it seems quite strange. Incidentally, the problem arose as I was studying the complex dynamics of Airy functions. My programs were running slower than I expected. I traced the problem down to this unexpected appearance arbitrary precision numbers. Mark McClure