  We introduce a new method for modelling the gravitational wave flux function
of a test-mass particle inspiralling into an intermediate mass Schwarzschild
black hole which is based on Chebyshev polynomials of the first kind. It is
believed that these Intermediate Mass Ratio Inspiral events (IMRI) are expected
to be seen in both the ground and space based detectors. Starting with the
post-Newtonian expansion from Black Hole Perturbation Theory, we introduce a
new Chebyshev approximation to the flux function, which due to a process called
Chebyshev economization gives a model with faster convergence than either
post-Newtonian or Pad\'e based methods. As well as having excellent convergence
properties, these polynomials are also very closely related to the elusive
minimax polynomial. We find that at the last stable orbit, the error between
the Chebyshev approximation and a numerically calculated flux is reduced, $<
1.8%$, at all orders of approximation. We also find that the templates
constructed using the Chebyshev approximation give better fitting factors, in
general $> 0.99$, and smaller errors, $< 1/10%$, in the estimation of the Chirp
mass when compared to a fiducial exact waveform, constructed using the
numerical flux and the exact expression for the orbital energy function, again
at all orders of approximation. We also show that in the intermediate test-mass
case, the new Chebyshev template is superior to both PN and Pad\'e approximant
templates, especially at lower orders of approximation.
