{"ID":2899389,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.02164","arxiv_id":"2507.02164","title":"Hardware-Accelerated Algorithm for Complex Function Roots Density Graph Plotting","abstract":"Solving and visualizing the potential roots of complex functions is essential in both theoretical and applied domains, yet often computationally intensive. We present a hardware-accelerated algorithm for complex function roots density graph plotting by approximating functions with polynomials and solving their roots using single-shift QR iteration. By leveraging the Hessenberg structure of companion matrices and optimizing QR decomposition with Givens rotations, we design a pipelined FPGA architecture capable of processing a large amount of polynomials with high throughput. Our implementation achieves up to 65x higher energy efficiency than CPU-based approaches, and while it trails modern GPUs in performance. Compared with state-of-the-art QR decomposition solutions, our design specificly optimize QR decomposition for complex-valued Hessenberg matrices up to size 6x6, exhibiting a moderate throughput of 16.5M QR decompositions per second, while prior works have predominantly focused on 4x4 general matrices.","short_abstract":"Solving and visualizing the potential roots of complex functions is essential in both theoretical and applied domains, yet often computationally intensive. We present a hardware-accelerated algorithm for complex function roots density graph plotting by approximating functions with polynomials and solving their roots us...","url_abs":"https://arxiv.org/abs/2507.02164","url_pdf":"https://arxiv.org/pdf/2507.02164v2","authors":"[\"Ruibai Tang\",\"Chengbin Quan\"]","published":"2025-07-02T21:42:39Z","proceeding":"cs.MS","tasks":"[\"cs.MS\",\"cs.AR\"]","methods":"[]","has_code":false}