CompensatedSummation in Total

*To*: mathgroup at smc.vnet.net*Subject*: [mg81075] CompensatedSummation in Total*From*: "David Park" <djmpark at comcast.net>*Date*: Mon, 10 Sep 2007 18:57:54 -0400 (EDT)

In the 'More Information' section of the help for Total it mentions that Method -> "CompensatedSummation" can be used as an option to reduce numerical error. But in the Options, Method section they use the option without quotation marks: Method -> CompensatedSummation. They actually both seem to work. I thought that the following example might be one that CompensatedSummation might help on since the sum tends to be much smaller than a sum of the absolute values. But I obtain exactly the same answer with or without CompensatedSummation - every time. So I wonder exactly what CompensatedSummation does for us? testlist = Table[RandomReal[{-1, 1}], {10000000}]; NumberForm[Total[testlist], 16] // Timing NumberForm[Total[testlist, Method -> "CompensatedSummation"], 16] // Timing testlist = Table[RandomReal[{-1, 1}], {10000000}]; NumberForm[Total[testlist], 16] // Timing NumberForm[Total[testlist, Method -> CompensatedSummation], 16] // Timing -- David Park djmpark at comcast.net http://home.comcast.net/~djmpark/