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For high resolution CT image reconstruction, algebraic reconstruction methods are widely used to get relatively good image quality. However, the slow speed has prohibited its routine use in clinical and industrial applications. Many GPU-based accelerated algebraic reconstruction methods have been presented for three-dimensional (3D) reconstruction in cone beam CT. But for the high resolution two-dimensional (2D) reconstruction in linear detector fan beam CT, such as industrial CT (ICT), the projection and back-projection are not convenient accelerated by texture hardware and 3D geometric transformation. In this paper, we focus on using the GPU SIMD parallel computing to accelerate the 2D algebraic reconstruction in linear detector fan beam CT. We will present the Bilinear Warping method for implementing the resample texture coordinates calculation, and give the GPU-based simultaneous algebraic reconstruction algorithm with OpenGL's evaluator of Bilinear Bezier surface. The implementation algorithm on HP workstation indicates a speedup of about 15, and the speedup increases with the reconstruction image size, that means this method will be suitable for high resolution CT image reconstruction in practice.