Mathematica: ill-conditioned linear system

[Asad Albostami]

Hi all, I have problem with regard to ill-conditioned linear system of solving sets of simultaneous equations using Mathematica program. I have tried my best to find a way to solve this but none was successful.
I got results from m =1 and n =1 until m = 7 and n = 7, i,e. the systems are well-conditioned. However, the problem started from when m = 9 and n = 9 due to ill-conditioned systems. Note that m = n = 1,3,5,6,7,9,...99. I am trying to find a treatment so that the matrix would not become a singular.

 

[Dale]

If the matrix is ill conditioned there is nothing that Mathematica can do other than to correctly report the ill conditioning. Basically, you are trying to divide by zero, and no math program can make that reasonable, the problem is the input itself not the program.

 

[Asad Albostami]

Thank you for your reply.
For my program I used a method it is called state space approach for finding the stresses through the thickness for any plate. From this method the plate has a top and bottom values and from finding the top stresses from an exponential matrix then I can calculate the bottom stresses but here I have a problem for a very big numbers that It gives me (For example if the top stresses is equal to 1 MPa the bottom stress is equal to 10^5). Please see the attached file it shows the formulas that I used. noting that the problem started when the looping numbers is increased (Because this method it is a summation of terms So more terms it means more accurate results).

 

[Dale]

The .pdf file doesn't work for me. However, in general you don't want to just blindly add 100 terms. You should specify some convergence criterion and stop adding terms as soon as the criterion is met or the criterion begins to indicate divergence. An ill conditioned matrix should cause any reasonable criterion to diverge, and a good criterion should stop adding terms before it becomes ill conditioned.