Re: How do twice Working Precision in square operation
- To: mathgroup at smc.vnet.net
- Subject: [mg86154] Re: How do twice Working Precision in square operation
- From: Steven Siew <siewsk at bp.com>
- Date: Mon, 3 Mar 2008 04:43:09 -0500 (EST)
- References: <200802291122.GAA19237@smc.vnet.net> <fqb8rc$n3f$1@smc.vnet.net>
In[3]:= n=12.34 n2=n*n Out[3]= 12.34 Out[4]= 152.276 At fist glance, it seems like you can get 6 digits of precision if you square a number with 4 digits of precision. But, if you assume the number 12.34 has a lower bound of 12.341 and a higher bound of 12.349 then you can see In[5]:= low=12.341 low2=low*low Out[5]= 12.341 Out[6]= 152.3 In[7]:= high=12.349 high2=high*high Out[7]= 12.349 Out[8]= 152.498 You can see that low2=152.3 and high2=152.49 , so you only get at most "3 to 4" digits of precision after you have square the number. You do not get 6 digits of precision. As Daniel Lichtblau from Wolfram has mentioned, increasing the precision artificially is nothing but self- deception. On Mar 1, 8:49 pm, Artur <gra... at csl.pl> wrote: > Who know how forced double numerical precision in operation ^2 or > triple in ^3 > e.g. we have number with precision 300 digits after comma and we do > square of this number > > N[-23.83242089169940112293636352304345516242356370829658528533245578869781207629749826968513219545485106785646817025052324254382671446440221122018213525849182937524917564915820784936033688847601879751439448736954164351572578669610243156800163244111408628195484090841094436992490050778`263.90219946983575^2,600] > > I want received WorkingPrecision->600 > > How do that on Mathematica ? > > BEST WISHES > ARTUR