06/06/2011, 11:01 AM
ive noticed we used both the terms vandermonde and carleman matrix.
ofcourse its carleman matrix and not vandermonde !
also note that the 2 matrix-method number must sum to 1 !!
0.580243966210
+
0.41975603379
=0.9999999999 = 1
simply because 1/(1+x) + 1/(1+(1/x)) = 1.
- which also shows the importance of the determinant !! -
because of this sum = 1 , the matrix methods cannot match the serial summation.(*)
this is similar to my determinant argument made before , just an equivalent restatement.
* the sum of both serials is related to the equation f(g(x)) = f(x) , whereas the sum of matrix methods just gives 1 for all x.
ofcourse its carleman matrix and not vandermonde !
also note that the 2 matrix-method number must sum to 1 !!
0.580243966210
+
0.41975603379
=0.9999999999 = 1
simply because 1/(1+x) + 1/(1+(1/x)) = 1.
- which also shows the importance of the determinant !! -
because of this sum = 1 , the matrix methods cannot match the serial summation.(*)
this is similar to my determinant argument made before , just an equivalent restatement.
* the sum of both serials is related to the equation f(g(x)) = f(x) , whereas the sum of matrix methods just gives 1 for all x.