Please also give Matlab solutions to the following problem.
Find the Pade approximation R_(5,4) (x) for f(x) = sin x. Plot the following graphs:
i) Comparison of R_(5,4) (x) versus f(x) = sin x, and
ii) the error E(x) = |R_(5,4) (x) - sin x|,
each on interval [-PI, PI].
Pade or rational functions are similar to approximations by Taylor polynomials. The method of finding a rational function from a given Taylor polynomial is described and several examples are worked in detail.