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a b s t r a c tWe show that a Fourier expansion of the exponential multiplier yields an exponential series that can compute high-accuracy values of the complex error function in a rapid algorithm. Numerical error analysis and computational test reveal that with essentially higher accuracy it is as fast as FFT-based Weideman's algorithm at a regular size of the input array and considerably faster at an extended size of the input array. As this exponential series approximation is based only on elementary functions, the algorithm can be implemented utilizing freely available functions from the standard libraries of most programming languages. Due to its simplicity, rapidness, high-accuracy and coverage of the entire complex plane, the algorithm is efficient and practically convenient in numerical methods related to the spectral line broadening and other applications requiring errorfunction evaluation over extended input arrays.

a b s t r a c tA new sampling methodology based on an incomplete cosine expansion series is presented as an alternative to the traditional sinc function approach. Numerical integration shows that this methodology is efficient and practical. Applying the incomplete cosine expansion we obtain a rational approximation of the complex error function that with the same number of the summation terms provides an accuracy exceeding the Weideman's approximation accuracy by several orders of the magnitude. Application of the expansion results in an integration consisting of elementary function terms only. Consequently, this approach can be advantageous for accurate and rapid computation.

Abstract. Argus 1000 is a new generation miniature pollution-monitoring instrument to monitor greenhouse-gas emission from the space. Argus was launched on the CanX-2 microsatellite April 28, 2008. Operating in the near infrared and in a nadir-viewing mode, Argus provides a capability for the monitoring of Earth-based sources and sinks of anthropogenic pollution. It has 136 near infrared channels in the spectral range of 0.9-1.7 µm with an instantaneous spatial resolution of 1.25 km. With a mass of just 228 g in flight-model configuration, the instrument is a demonstrator for a future micro-satellite network that can supply near-real time monitoring of pollution events in order to facilitate the detection of the sources causing climate change. In this Letter, we describe the instrument, the analysis concept behind Argus 1000 and its in-orbit performance. Recent spectral data taken over Ontario, Canada, are presented.

Recently we developed a new sampling methodology based on incomplete cosine expansion of the sinc function and applied it in numerical integration in order to obtain a rational approximation for the complex error function w (z) = e −z 2 1 + 2i √ π z 0 e t 2 dt , where z = x + iy. As a further development, in this work we show how this sampling-based rational approximation can be transformed into alternative form for efficient computation of the complex error function w (z) at smaller values of the imaginary argument y = Im [z]. Such an approach enables us to avoid poles in implementation and to cover the entire complex plain with high accuracy in a rapid algorithm. An optimized Matlab code utilizing only three rapid approximations is presented.