Computational math

Computational math

Consider the Pade’ approximation to the function F(x)

F : [0 , 1] à R , f Î C∞ ( f(n) (x) exists and continuous ” n Î N )

Of the p(x) =

=

F(x) @ p(x) f(x) can be approximated by p(x)

Consider f(x) = ex , f Î C∞ (R )

Now:

1- Determine the coefficients {an}4n=0 and {bm}3m=1 using Maclaurian series expansion ( Taylor at x = 0 ) optimization.

2- Construct the linear system of equation Ax =b .