Recent advances in technology coupled with the progress of observational radio astronomy methods resulted in achieving a major milestone of astrophysics - a direct image of the shadow of a supermassive black hole, taken by the Earth-based Event Horizon Telescope (EHT). The EHT was able to achieve a resolution of ∼20μas, enabling it to resolve the shadows of the black holes in the centres of two celestial objects: the supergiant elliptical galaxy M87 and the Milky Way Galaxy. The EHT results mark the start of a new round of development of next generation Very Long Baseline Interferometers (VLBI) which will be able to operate at millimetre and sub-millimetre wavelengths. The inclusion of baselines exceeding the diameter of the Earth and observation at as short a wavelength as possible is imperative for further development of high resolution astronomical observations. This can be achieved by a spaceborne VLBI system. We consider the preliminary mission design of such a system, specifically focused on the detection and analysis of photon rings, an intrinsic feature of supermassive black holes. Optimised Earth, Sun–Earth L2 and Earth–Moon L2 orbit configurations for the space interferometer system are presented, all of which provide an order of magnitude improvement in resolution compared to the EHT. Such a space-borne interferometer would be able to conduct a comprehensive survey of supermassive black holes in active galactic nuclei and enable uniquely robust and accurate tests of strong gravity, through detection of the photon ring features.

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The tridiagonal solver is an important kernel in many scientific and engineering applications. Although quite a few parallel algorithms have been exploited recently, challenges still remain when solving tridiagonal systems on many-core architectures. In this paper, quantitative analysis is conducted to guide the selection of algorithms on different architectures, and a fast register-PCR-pThomas algorithm for Intel MIC architecture is presented to achieve the best utilization of in-core vectorization and registers. By choosing the most suitable number of PCR reductions, we further propose an improved algorithm, named register-PCR-half-pThomas algorithm, which minimizes the computational cost and the number of registers for use. The optimizations of manual prefetching and strength reduction are also discussed for the new algorithm. Evaluation on Intel Xeon Phi 7110P shows that our register-PCR-pThomas can outperform the MKL solver by 7.7 times in single precision and 3.4 times in double precision. Moreover, our optimized register-PCR-half-pThomas can further boost the performance by another 43.9% in single precision and 20.4% in double precision. Our best algorithm can outperform the latest official GPU library (cuSPARSE) on Nvidia K40 by 3.7 times and 2.4 times in single and double precision, respectively.@en