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#51 Re: Help Me ! » Wronskian use identities ! » 2013-12-11 09:43:48
They are two solutions of the differential equation for which it's true that v1/v2 is not constant.
Exactly!!The Wronskian is:
| v1(0) v2(0) |
| v1'(0) v2'(0) |
#52 Re: Help Me ! » Wronskian use identities ! » 2013-12-11 09:24:04
The Wronskian is
|u(0) v(0)|
|u'(0) v'(0) |
But...how can I show that there are constants
#53 Help Me ! » Wronskian use identities ! » 2013-12-11 06:35:47
- evinda
- Replies: 63
Hello!!! 
Could you help me at the following exercise?
Let
and that each solution of the differential equation has the form:.
#54 Coder's Corner » Myhill-Nerode theorem » 2013-12-08 05:47:00
- evinda
- Replies: 0
Hi
I have a question..How could I show that the language L={xy^{n}zy^{n}w: x,z,w in Σ*, y in Σ, z does not contain y, and n>=0} is not regular, using the Myhill-Nerode theorem?
#55 Re: Computer Math » Not sure if output is right » 2013-12-04 09:43:24
I get this message:??? DIGITS:=25
|
Error: The expression to the left of the equals sign is not a valid target for an
assignment.
But...anyway...I will let it like that...I have a last question..Could you tell me which is the iteration matrix ,for example of the hilbert matrix with a specific dimension,or for another matrix using the gauss-seidel method,and which it is using the jacobi method ,so I can check if my result is right???
#56 Re: Computer Math » Not sure if output is right » 2013-12-02 10:48:46
Why not? What are you entering for the matrix?
I wrote this:DIGITS:=hilb(15) and I get Error: The expression to the left of the equals sign is not a valid target for an
assignment.
#57 Re: Computer Math » Not sure if output is right » 2013-12-02 08:43:45
http://www.mathworks.com/help/symbolic/ igits.html
The examples on that page do not work?
They work...But I can't apply them at a matrix 
#58 Re: Computer Math » Not sure if output is right » 2013-12-02 08:05:29
I get this error message:Error: The expression to the left of the equals sign is not a valid target for an
assignment.
I would like to ask you also something else..Is this right that the spectral radius of the iteration matrix of the 250x250 Hilbert Matrix,when we apply the Gauss-Seidel method is 1,and when we apply the Jacobi method 217.3320?
#59 Re: Computer Math » Not sure if output is right » 2013-12-01 10:24:06
Something is wrong with your program. That converges for me. Are you setting initial conditions to [0,0,0,0]?
Check this page to see how to increase Matlabs precision:
http://www.mathworks.com/help/symbolic/ … igits.html
See you a bit later, I need some rest.
I used the command digits bit I didn't get any result!!! 
why??
#60 Re: Computer Math » Not sure if output is right » 2013-12-01 08:13:31
You have a 4 on the diagonal and 1 on the other 2 diagonals? That matrix according to some books is diagonally dominant. This makes convergence easy in the Gauss Seidel method.
I understand...
But we are straying from the point of this thread. Did you try post #18's matrices? Did they converge for you? What did you notice about the new A?
No,the matrix of post #18 does not converge,neither using the jacobi,nor the gauss-seidel method..
#61 Re: Computer Math » Not sure if output is right » 2013-12-01 07:17:24
I believe that there is a simple answer to that.
Could you tell me,which it is??
:
#62 Re: Computer Math » Not sure if output is right » 2013-12-01 07:13:56
There are other reasons for divergence. Poor initial conditions is one reason. The condition number for that matrix if I remember was around 500. That is not too bad.
The condition number for n=500 is for example 1.2550e+005 ..
So,is it right that the methods do not converge for this matrix ??
Because,for example,both of the methods do converge for an other tridiagonal matrix,that has the number 4 at the main diagonal,1 at the first diagonal below this and also 1 at the first diagonal above this.
Which is the difference??
#63 Re: Computer Math » Not sure if output is right » 2013-12-01 06:50:31
The matrix is already diagonally dominant. There is nothing else to be done with it. Numerical methods are not like Algebra. They do not always work!
So,why do the methods not converge,although the matrix is diagonally dominant??
#64 Re: Computer Math » Not sure if output is right » 2013-12-01 06:40:45
You are not following. Nothing on this earth will ever get the answer to that linear system using Matlab's precision.
And what if I want to apply the methods at a 250x250 tridiagonal matrix with the number 2 at the main diagonal,-1 at the first diagonal below this and also -1 at the diagonal above this?Because both of the methods do not converge for this matrix..
#65 Re: Computer Math » Not sure if output is right » 2013-12-01 06:32:09
You can not do it for a general case. Each one is different and it may not work next time. Numerical work is a hands on skill. You must experiment.
How can I rearrange,for example,a 250x250 Hilbert Matrix??
#66 Re: Computer Math » Not sure if output is right » 2013-12-01 05:19:03
Use this matrix here:
How did you rearrange the matrix??Because I have to do this for the general case,and not for a special matrix..
#67 Re: Computer Math » Not sure if output is right » 2013-12-01 04:12:07
You can rearrange the matrix until it is diagonally dominant or close to it.
Can you do that or do you require help?
I don't know how to do this 
I think I need some help..
#68 Re: Computer Math » What have I done wrong?? » 2013-12-01 01:51:34
Hi evinda;
You do not have the b vector to copy and paste? I am not seeing how to use that sum?!
You want to know how I wrote it in my code??
#69 Re: Computer Math » What have I done wrong?? » 2013-12-01 01:13:41
Yes, it would require you to work to 400 digits of precision to get an answer that had 20 correct digits. If you can not work to that many digits the answers obtained will be meaningless.
If you supply the b, I can do the calculations for you.
#70 Re: Computer Math » What have I done wrong?? » 2013-12-01 00:28:25
Why??Because of the fact that the Hilbert Matrix is very ill-conditioned??
#71 Re: Computer Math » What have I done wrong?? » 2013-11-30 23:25:48
I do not program in Matlab so you will have to consult the help.
Just what I said Matlab is interpreting a nearly singular matrix for a singular matrix.
Unless you can access the higher precision routines that Matlab has ( and they are pretty skimpy ) a big Hilbert will be out.
I haven't found yet such a routine of Matlab..
And something else...Why when I find the error ||x_{k}-D|| of the last iteration of the methods,for n>=250,at the Jacobi method I get the result Nan and at the Gauss-Seidel method I get a real number???
(D is the exact result of the linear system)
#72 Re: Computer Math » What have I done wrong?? » 2013-11-30 07:24:08
One with a very high condition number or one with the determinant being nearly 0.
You are not using Matlab well enough, read up on these suggestions:
The Symbolic Toolbox and its vpa (variable precision arithmetic) commands if you want to accurately work with a large Hilbert Matrix.
There is also the bicgstab command.
If you can not get any of these to work then give me the column vector b and I will solve the system using the tools I have.
Now,I wanted to calculate the determinant and the result is: det(H)=0.. 
So,you mean,that I should write it for example like that: vpa(hilb(n))? Or with an other way?? :/
#73 Re: Computer Math » What have I done wrong?? » 2013-11-30 05:43:29
Could you explain what a nearly singular matrix is??
#74 Re: Computer Math » What have I done wrong?? » 2013-11-30 05:08:28
Is it like division by 0???Or not???
#75 Re: Computer Math » What have I done wrong?? » 2013-11-30 04:23:41
So you see .3333 is not 1 / 3. When you did a calculation with it the error was magnified until it has a difference of 30.
I understand..And how can I explain why my result is Nan??