Control Systems in Practice: Why Padé Approximations Are Great!

(a) Find the pade approximation to e^2x of degree 2 with n = 1 and m = 1 we need to choose p0, p1, q1 so that the coefficients of x^k for k = 0, 1, 2 are 0 in the expression (1 2x ((2x)^2)/(2) ((2x)^3)/(6) ...)(1 q1x) = (p0 p1x) The pade approximation is r(x) = (p(x))/(q(x)) Step 2/11 Let us assume that q0 = 1 Now comparing both side the coefficients of x^2, x^1 & x^0 We get x^0: p0 = 1......(1) x^1: p1 = q1 2......(2) x^2: 0 = 2q1 2......(3)