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We introduce a new method for modelling the gravitational wave flux functionof a test-mass particle inspiralling into an intermediate mass Schwarzschildblack hole which is based on Chebyshev polynomials of the first kind. It isbelieved that these Intermediate Mass Ratio Inspiral events (IMRI) are expectedto be seen in both the ground and space based detectors. Starting with thepost-Newtonian expansion from Black Hole Perturbation Theory, we introduce anew Chebyshev approximation to the flux function, which due to a process calledChebyshev economization gives a model with faster convergence than eitherpost-Newtonian or Pad\'e based methods. As well as having excellent convergenceproperties, these polynomials are also very closely related to the elusiveminimax polynomial. We find that at the last stable orbit, the error betweenthe Chebyshev approximation and a numerically calculated flux is reduced, $<1.8%$, at all orders of approximation. We also find that the templatesconstructed using the Chebyshev approximation give better fitting factors, ingeneral $> 0.99$, and smaller errors, $< 1/10%$, in the estimation of the Chirpmass when compared to a fiducial exact waveform, constructed using thenumerical flux and the exact expression for the orbital energy function, againat all orders of approximation. We also show that in the intermediate test-masscase, the new Chebyshev template is superior to both PN and Pad\'e approximanttemplates, especially at lower orders of approximation.Comment: 9 Pages, Accepted for publication, Proceedings of GWDAW 10, Special  edition of Classical and Quantum Gravit

Modelling the post-Newtonian test-mass gravitational wave flux function for compact binary systems using Chebyshev polynomials