Message Boards Message Boards

0 Replies
0 Total Likes
View groups...
Share this post:

Integration warning: Merely an error estimate, or an upper bound?

Posted 4 months ago

This integral

i1 = NIntegrate[ Sqrt[1 + (x^6 + y^6)/(1 - x^4 - y^4)^(3/2)] ,
  {x, 0, 1/3^(1/4)}, {y, 0, x}, WorkingPrecision -> 100, PrecisionGoal -> 40 ]

returns, roughly, 0.30155... along with the warning "NIntegrate obtained 0.30155... and 3.20396...*10^-16 for the integral and error estimates"

If the estimate 3.20396...*10^-16 is an upper bound, this is valuable information.

But if the actual error could be larger than this, then this number is not useful (to me).

Which is it? A mere estimate of the error, or an upper bound on the error?

POSTED BY: Robert Baillie
Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Reply Preview
or Discard

Group Abstract Group Abstract