Pulsar Timing Array (PTA) experiments are expected to be sensitive to
    gravitational waves (GWs) emitted by individual supermassive black hole
    binaries (SMBHBs) inspiralling along eccentric orbits. We compare the
    computational cost of different methods of computing the PTA signals induced by
    relativistic eccentric SMBHBs, namely approximate analytic expressions, Fourier
    series expansion, post-circular expansion, and numerical integration. We show
    that the fastest method for evaluating PTA signals is by using the approximate
    analytic expressions, providing up to a $\sim$50 times improvement in
    computational performance over the alternative methods. We investigate the
    accuracy of the approximate analytic expressions by employing a mismatch metric
    valid for PTA signals. We show that this method is accurate within the region
    of the binary parameter space that is of interest to PTA experiments. We
    introduce a spline-based method for further accelerating the PTA signal
    evaluations for narrow-band PTA datasets. These results are crucial for
    searching for eccentric SMBHBs in large PTA datasets. We have implemented these
    results in the GWecc package and can be readily accessed from the popular
    ENTERPRISE package to search for such signals in PTA datasets.

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