The infnorm in the numapprox package is what I was using to find the supremum on the main diagonal, but I noticed that they have done something new with it in Maple 10, I just haven't had time to look at it the new feature.
I have some local government matters to attend to today, so I won't be able to play with the worksheet you sent for a bit. It looks quite interesting, though, and I look forward to digging into it.
With regard to being notified of posts, I thought that when we are writing a basenote or a reply, there is a little box near the bottom of the page that we can check to be notified of updates. Sad to say that I don't see it at the bottom of this page on which I am replying... There is also a "my subscriptions" link in the Navigation bar at top left, which appears to offer some control over notifications. I don't remember using it, though, so there is probably more than one way to do it.
- Jimmy

The infnorm in the numapprox package is what I was using to find the supremum on the main diagonal, but I noticed that they have done something new with it in Maple 10, I just haven't had time to look at it the new feature.
I have some local government matters to attend to today, so I won't be able to play with the worksheet you sent for a bit. It looks quite interesting, though, and I look forward to digging into it.
With regard to being notified of posts, I thought that when we are writing a basenote or a reply, there is a little box near the bottom of the page that we can check to be notified of updates. Sad to say that I don't see it at the bottom of this page on which I am replying... There is also a "my subscriptions" link in the Navigation bar at top left, which appears to offer some control over notifications. I don't remember using it, though, so there is probably more than one way to do it.
- Jimmy

Hi Will,
Thanks for the edit to my post. It is true that my post did not use filters to process the 2D math; that is because when I tried, it failed. And I certainly understand the difficulty of the sheer length of the expression, and appreciate your clarifying it for other readers. Unfortunately, the 2D math in the second expression does not match the text version which appears just above it. Could you please change it to match the expression that I sent?
One other thing. Because a casual reader may interpret "Fix" to mean that you have solved my problem of converting rational exponents to floating point, I wonder if you could qualify your title a bit.
Thanks again,
- Jimmy
Thank you again,
- Jimmy Benjamin

Hi Will,
Thanks for the edit to my post. It is true that my post did not use filters to process the 2D math; that is because when I tried, it failed. And I certainly understand the difficulty of the sheer length of the expression, and appreciate your clarifying it for other readers. Unfortunately, the 2D math in the second expression does not match the text version which appears just above it. Could you please change it to match the expression that I sent?
One other thing. Because a casual reader may interpret "Fix" to mean that you have solved my problem of converting rational exponents to floating point, I wonder if you could qualify your title a bit.
Thanks again,
- Jimmy
Thank you again,
- Jimmy Benjamin

Hi Axel,
I'll defer to Fred on the more abstract first question, but Carvajal seems to use a discrete grid of function values (25, doubling under certain circumstances), and uses the grid to estimate the point at which the supremum occurs. I think he choses the max of the 25, rather than interpolating with those points. I think the confinement stage of his algorithm seeks to identify any "surprise" supremums, with a heuristic of doubling the number of points when too many of them were zeros. Is that how you read it?

Hi Axel,
I'll defer to Fred on the more abstract first question, but Carvajal seems to use a discrete grid of function values (25, doubling under certain circumstances), and uses the grid to estimate the point at which the supremum occurs. I think he choses the max of the 25, rather than interpolating with those points. I think the confinement stage of his algorithm seeks to identify any "surprise" supremums, with a heuristic of doubling the number of points when too many of them were zeros. Is that how you read it?

Thank you for the good ideas, Axel -- that was a nice change of variables. High precision is needed because the integral is an addend of a rather ill-conditioned sum; with adequate precision, I don't need to convert the problem to another that has unpleasant sigularities.. but I should resist basenote drift.
I'm sure that you're right about the release of a G-N toolbox; we probably aren't the only ones who will look forward to it.
I'll chew on your reforumlation and / or take a stab at implementing the G-N for this special case. I'll let you know how it turns out. If any other thought cross your mind, feel free to post / write.
For the record, I edited the basenote so that the limits of integration were properly typeset. Sorry for it being hard to read last night.
- Jimmy

Thank you for the good ideas, Axel -- that was a nice change of variables. High precision is needed because the integral is an addend of a rather ill-conditioned sum; with adequate precision, I don't need to convert the problem to another that has unpleasant sigularities.. but I should resist basenote drift.
I'm sure that you're right about the release of a G-N toolbox; we probably aren't the only ones who will look forward to it.
I'll chew on your reforumlation and / or take a stab at implementing the G-N for this special case. I'll let you know how it turns out. If any other thought cross your mind, feel free to post / write.
For the record, I edited the basenote so that the limits of integration were properly typeset. Sorry for it being hard to read last night.
- Jimmy