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Condition Number and Significant Digits

  1. May 3, 2014 #1
    1. The problem statement, all variables and given/known data
    IF A is nxn matrix, and k(A)=||A||||A^-1|| then a large k(A) means the solution has more significant digits than is k(A) were small true or false?


    2. Relevant equations



    3. The attempt at a solution
    Well k(A) is defined as 10^(k) right so the larger the condition number the more significant digits that you shouldnt trust. So if I had 10^(16) I would have approximatley 16 sig figs that I shouldnt use. Therefore I would think the answer is true if condition number is large then there will be more significant digits just not usable ones right?
     
  2. jcsd
  3. May 3, 2014 #2
    I get that the small the k(A) the more reliable a solution is meaning it would have to have an a good amount of sig figs such that it is accurate so maybe it is false hmmm I dont know?
     
  4. May 4, 2014 #3
  5. May 4, 2014 #4
    Ok, I will give that a look.
     
  6. May 4, 2014 #5
    So it is saying that the higher the condition number the larger the error which is what I thought. So I guess what I am supposed to take from this is that the smaller the condition number the more precise the solution, however this problem specifies significant digits not precision so I am gonna go with True.
     
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