please re-think your question: I did not say it is a correlation matrix ...

www.optimization-online.org/DB_HTML/2003/09/729.html

it makes it symmetric and you should check whether your matrices satisfy M = Transpose(M)

For your actual problem: this may be caused by numerical rounding errors, you may gogle for 'nearest positive symmetric' or similar.

it makes it symmetric and you should check whether your matrices satisfy M = Transpose(M)

For your actual problem: this may be caused by numerical rounding errors, you may gogle for 'nearest positive symmetric' or similar.

As you have already seen there is no solution for a,b which holds for all x.

In Math terms your task might be as follows: 

Take the (square-integrable, real-valued) functions on the interval [0,Pi/2]
(this is a vector space). 

Given two functions f and g write <f,g> = Int( f(x)*g(x), x = 0 .. Pi/2 ).
Then this is a inner product and sqrt( <f,f> ) is the norm of an element,
norm(f) is a real-valued function on 0 ... Pi/2.

Usually it is devided by the length of the interval to have norm(id) = 1.

You may look up for L2-Space in your lectures or at Wikipedia or whatever.

It is a generalization of the usual Euklidean norm, it 'measures' distance
from zero.

Now you are given the function f:= x -> a*sin(2*x) - b*sin(4*x) - sin(x),
it actually depends on the parameters a and b.

There is no pair a,b that this function is zero, so norm(f) can not be 0.
But one can hope to find a,b such that the norm is minimal.

1) Write down the norm for f and compute it with Maple.
   The solution depends on a and b.
2) What do you remember as conditions on a and b that this
   is 'minimal' ? Write that down using Maple (look up the
   commands 'diff', 'Diff' and 'D').
3) Find a solution (look up 'solve', 'simplify/trig') in
   terms of a and b.
4) That solution gives a function on 0 ... Pi/2. How do you
   write that using Maple? What is the norm of that function?
5) Give a graphic comparing sin(x) and a*sin(2*x) - b*sin(4*x)
   to show them.

www.mapleprimes.com/mapleprimes-forums/general-discussion/mapleprimes-suggestions contains a whole bunch ...

After dividing by H and renaming you consider sin(x)=a*sin(2*x) - b*sin(4*x).

Now look at it in 0 and in Pi/2, where the latter will give you 1 = 0. That
together with the title of your post may motivate you to aks the question in
a more precise way.

So what is the actual task you have to solve? What is it in Math terms?

For the above I guess the answer could be: a = 8/3/Pi and b = 16/15/Pi.

You are just confirming what I was afraid of.

PS: 3 hits / day are really cool, if Google finds that page just after entering 'Central Difference Maple'  ...

"a vital resource for our users" - so nobody can be bored

"highest use occurs during the school periods" - hence leave answering questions to experienced users, do never spend the valuable time of staff?

"MaplePrimes make all of this information easily accessible and result in people finding answers to their questions very quickly" - then those (me as well) wishing a reasonable search functionality have no reason to demand that

...

Good to know. Such an answer is convincing and explains much to me, really. And at a 3rd thought I find it even hilarious.

Personally I am not so much interested in design question (my feeling is, that I do not know enough in a systematical sense and what ever was brought up from a users view seems to be taken not quite serious by semi official answers [no, not you or others here] and thus lost almost any interest on that for this forum). However I tried to learn from those discussions, at least.

For me Maple is more interesting in applying it to Math or 'Engineering' problems.

But much of concurrent questions is on handling (even very basic one, where I intend to answer 'read the f... manual', others remind me of my troubles to stumble into that mighty and sometimes a bit self-willed software system) and that really should be answered by Maple stuff as a kind of 1st level support:

If this is left to 'senior' users it saves money, ok. But those will loose interest.

Anyway: I have to admit that I concurrently do not contribute that  much for Math questions (asking or answering), but that is 'seasonal'. Still I check the page ~ 2 times the day.

PS: missing a link to concurrent contributions (http://www.mapleprimes.com/tracker), a clear link to Online Maple (alwys forget it) and a reasonable search functionality here (but see above: I am bored by montonous regrets ...)

google leads me to http://www.mathematik.uni-erlangen.de/~ruppert/WS0607/SHA_ma, but I did not scan through his lectures

google leads me to http://www.mathematik.uni-erlangen.de/~ruppert/WS0607/SHA_ma, but I did not scan through his lectures

Alec, I will pick up that the other days, interesting (recompiling is a mess, yes)

Alec, I will pick up that the other days, interesting (recompiling is a mess, yes)

MS has problems with it now and then - even with internet URLs (where that should not be used, but MS 'introduced' that).

For example if you install Maple into its standard directory, then there wil be a blank in it (I overwrite that always). If then you want to use OpenMaple and link to libs the MS compiler fails (at least it was in MSVC, have not checked for newer versions, since I change to proper directory names).

Dito all my directory holding executables are without blank (programs, not program files etc), at least an underscrore will do.

Only for actual files I gave up and meanwhile use long names with blanks.

MS has problems with it now and then - even with internet URLs (where that should not be used, but MS 'introduced' that).

For example if you install Maple into its standard directory, then there wil be a blank in it (I overwrite that always). If then you want to use OpenMaple and link to libs the MS compiler fails (at least it was in MSVC, have not checked for newer versions, since I change to proper directory names).

Dito all my directory holding executables are without blank (programs, not program files etc), at least an underscrore will do.

Only for actual files I gave up and meanwhile use long names with blanks.