# Calculate number of significant figures EFFECTIVELY obtained

1. Oct 20, 2012

### libelec

1. The problem statement, all variables and given/known data
Solve the following equation system using the Gauss-Seidel method, and the convergence criteria || x(k) - x(k-1) || <= 0.5 * 10-2. For the arithmetics, use a number of significant digits that will allow you to get a result with 3 significant digits. Must not iterate more than 5 times.

3.210*a + 0.943*b + 1.020*c = 2.300
0.745*a - 1.290*c = 0.740
0.875*a - 2.540*b + 0.247*c = 3.390

Calculate the number of significant digits effectively obtained for each vector element, and conclude if the convergence criteria was appropriate to get 3 significant digits.

3. The attempt at a solution

After having obtained the solution through the Gauss-Seidel method, I found this question odd. I never heard of a way to calculate the number of significant digits one effectively found, rather use as many significant digits as the error boundary allows you.

I thought two possible interpretations:

a) It's asking me if the approximation of the absolute error (|| x(k) - x(k-1) ||) is at or smaller than 0.5 * 102 for each component. Which I find weird, because if one got the solution with that convergence criteria, you are certain that, at least, each component has 3 significant numbers.

b) Like with iterative refinement, calculate δ$\bar{x}$ (Ax - A$\bar{x}$) and get the number of significant digits through the log(K(A)), where K(A) is the condition of the matrix A. The results I found make no sense, because I get something lower than 1, and I've never applied this to anything other than iterative refinement of direct methods.

Any ideas?

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted