4 Responses to “order of magnitute(big Oh)”

1. admin says:

   July 29 at 1:03 pm

   On Sat, 17 Dec 2005, oercim wrote:
   > What is the order of magnitute(big Oh) of the below expression,

   >        sum(a^i* (n^2-i^2)),  i=n, n+1, …..,n   for |a|<1

   >       here sum refers the sigma notation. Thanks alot.

   As the sum is on i and it goes from n to … n, there is but
   one term in the sum, namely when i = n.  Thus
           sum(…) = a^n (n^2 – n^2) = 0

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2. admin says:

   July 29 at 1:03 pm

   sorry, I made a mistake. It is from n to 2n. thanks
3. admin says:

   July 29 at 1:03 pm

   On Sat, 17 Dec 2005, oercim wrote:
   > sorry, I made a mistake. It is from n to 2n. thanks

   I’ve not the time nor the inclination for the clerical chore of back
   tracking the thread to reconstruct the line of thought.  If you want
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   answers from what I remember, then include the context pertinent to your
   reply and to whom your are talking.

   Please learn and use better math group manners as demonstrated
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4. admin says:

   July 29 at 1:03 pm

          Hello, my main problem is  much difficult. I am stuck with it.
   Let   C and A be n*n matrices which have the below pattern.
   

        |   1       0     0   0  . .. |          |    b  1   1   1 .. |
    C=|   a       1     0   0   …|  ,  A=|     1  b   1  1   ..|
        |   a^2    a     1   0   …|          |     1  1   b  1  … |
        |   a^3    a^2  a   1   …|          |    1  1   1  b   .. |
           ..        ..    ..   … . ..               .. …  …  …

              Let define as M=C’ACC’AC.
            My problem is to find the asymptotic behaviour of
            trace(M) which is eqaul to sum((i=1 to n)(j=1 to n)(Mij^2))
   as n increases. I tested this in matlab.It is O(n^2). But I can’t
   derive it anatically. It seemed to me very complicated. Can someone
   help please? Thanks.