Carl Love

## 26513 Reputation

11 years, 187 days
Himself
Wayland, Massachusetts, United States
My name was formerly Carl Devore.

## Oops, I meant Shift-Enter also....

Oops, I meant Shift-Enter also. Control-Enter gives me the page break in both 1D and 2D. Shift-Enter gives me a newline in both, but no extra space.

Could you please restate the problem? Are you using LL and S interchangeably? Are you using "list" and "set" interchangeably? Does "nonoverlapping" mean "has empty intersection"? Do you think that the LogicProblem package in the Maple Application Center (the link you gave) can help in solving this problem?

Edit: Corrected spelling of "interchangeably"

## Web page says "only"...

There are only two complete sentences on the web page in question, and I cut-and-paste them right here: "Maple T.A. is the only testing and assessment system designed for courses involving mathematics. In this video, you’ll see 10 reasons why Maple T.A. is the best choice for your math, engineering, and science courses."  I am not taking sides on this issue, as I know nothing about WebAssign, and very little about MapleTA. I'm just pointing out that they clearly say "only", as was claimed.

## Solution unique upto a common multiple...

Ah, I see. Of course the solution can only be unique upto a common multiple of numerator and denominator.

## Solution unique upto a common multiple...

Ah, I see. Of course the solution can only be unique upto a common multiple of numerator and denominator.

## Please clarify "One more difficulty"...

@Markiyan Hirnyk

I don't understand the point you are trying to make in "One more difficulty". Why did you make eq3 and eq4 the same?

Also, it would useful to sparsify and block-diagonalize the system of linear equations (especially since an exact  solution is required, rather than floating point) by choosing 0 as an evaluation point as much as possible.

## Please clarify "One more difficulty"...

@Markiyan Hirnyk

I don't understand the point you are trying to make in "One more difficulty". Why did you make eq3 and eq4 the same?

Also, it would useful to sparsify and block-diagonalize the system of linear equations (especially since an exact  solution is required, rather than floating point) by choosing 0 as an evaluation point as much as possible.

## 1307 is suspicious...

Something that is suspicious to me (and this may be the impetus which caused the OP to originally question the final result) is that the value 1307, which appears in the definition of B and as the upper limit of integration, is suspiciously close to, but not equal to, the value of A at which the abs would make a difference; which you computed to be 1309.46. Replacing both 1307s with this makes a significant difference (rel. err. = 1.6%) in the final result.

## 1307 is suspicious...

Something that is suspicious to me (and this may be the impetus which caused the OP to originally question the final result) is that the value 1307, which appears in the definition of B and as the upper limit of integration, is suspiciously close to, but not equal to, the value of A at which the abs would make a difference; which you computed to be 1309.46. Replacing both 1307s with this makes a significant difference (rel. err. = 1.6%) in the final result.

## Please clarify "power is limited"...

When you say "their power is limited ... [to], for instance, no more than 3", do you mean that the total degree of the polynomials is at most 3? Or do you mean that the degree, or power, of each individual variable is at most 3?

## What do you mean by "solve"?...

What do you mean by "solve"? Do you mean "approximate"? What is the "it" about whose truth you ask?

You've given some Maple commands, which work correctly. But what's the point of only using three terms of your series? Why aren't you satisfied with the output?

## No, it's not too large...

To address directly the OP's issues:

mike_a wrote:

> I noticed some strange things with the list/table carrying my complex points. If I ask for individual values, like T[20], it won't give the correct value, but if I ask for a range, like T[1..20], it will display the correct values.

You'll have to post some code so we can figure out what's going on. But I'll tell you right off that your problem has nothing to do with the size of your data set.

> I get an error when trying to use complexplot saying either invalid range, if I don't have a range for the 2nd and 3rd argument, or else Error, (in plot) procedure expected, as range contains no plotting variable. I assume that there's some problem with the table being too large and not a problem with the complexplot command

No, it has nothing to do with the table being too large. But you'll need to post some code so that we can figure out the actual problem.

First work out these indexing problems on a much smaller version of your plot before moving on to the million-point plot.

## Summary...

To summarize what you said, for those who may have trouble reading it: You are trying to solve, using a least-squares method, a linear system A.X = B, where A has dimensions 1201 x 800 and B is a column vector. You have a tried an ad hoc method that involves explicitly inverting an 800 x 800 matrix, but ran out of memory.

You wrote:

> A^T*A*X=A^T*X.  let M=A^T*A.  M*X=A^T*X  finally  X=M^-1 * A^T*X

That's supposed to be B, not X, on the right sides of those equations! I hope that was just a typo in your post and not in your Maple code!

Several questions before we go any further:

1. Is A a hardware floating point matrix?
2. What percentage of the elements of A are non-zero? A rough estimate is fine.
3. Have you tried LinearAlgebra:-LeastSquares?
4. Can you make a smaller version of this problem that we can practice with before doing the full 1201 x 800?

## Plot of Preben's one-term approximation...

A plot shows that Preben's one-term approximation is excellent even for x close to -2, and the original is visually indistinguishable from the approximation for x < -3.2. The plot below uses A and res as defined in Preben's code. If Digits, numpoints, and adaptive are not reduced from their default values (as I have done below), Maple will take a very long time to do the numerical integrations.

Digits:= 6:
plot([op(1,res), A], x= -3.3..-2.1, numpoints= 50, adaptive= 4);

I had originally plotted down to x = -10, but then it difficult to even see that there are two curves because they are so close.

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