Bessel functions often arise in advanced engineering analyses such as the study of electric fields. Here are some selected values
for the zero-order Bessel function of the first kind:
x 1.8 2.0 2.2 2.4 2.6
J1(x) 0.5815 0.5767 0.5560 0.5202 0.4708
Estimate J1(2.1) using third- and fourth-order interpolating polynomials. Generate the interpolating poly- nomials by forming linear systems Ax = b and solving for the polynomial coefficient vector x. Determine the percent relative error for each case based on the true valued, which can be determined with MATLAB's built-in function besselj, i.e. >> J = besselj(1,2.1).