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This paper describes TANOR, an automated framework for designing hardware accelerators for numerical computation on reconfigurable platforms. Applications utilizing numerical algorithms on large-size data sets require high-throughput computation platforms. The focus is on N-body interaction problems which have a wide range of applications spanning from astrophysics to molecular dynamics. The TANOR design flow starts with a MATLAB description of a particular interaction function, its parameters, and certain architectural constraints specified through a graphical user interface. Subsequently, TANOR automatically generates a configuration bitstream for a target FPGA along with associated drivers and control software necessary to direct the application from a host PC. Architectural exploration is facilitated through support for fully custom fixed-point and floating-point representations in addition to standard number representations such as single-precision floating point. Moreover, TANOR enables joint exploration of algorithmic and architectural variations in realizing efficient hardware accelerators. TANOR's capabilities have been demonstrated for three different N-body interaction applications: the calculation of gravitational potential in astrophysics, the diffusion or convolution with Gaussian kernel common in image processing applications, and the force calculation with vector-valued kernel function in molecular dynamics simulation. Experimental results show that TANOR-generated hardware accelerators achieve lower resource utilization without compromising numerical accuracy, in comparison to other existing custom accelerators.