2019-01-012024-05-15https://scholars.lib.ntu.edu.tw/handle/123456789/663136摘要：本計畫旨在解決大規模數值模擬和大數據分析所涉及的矩陣計算問題。 我們打算開發新穎的平行和可擴展算法，以減少浮點計算和數據傳輸成本，實現高效且強大的軟體程式庫，並應用這些程式庫來解決一些最關鍵的科學問題。 主要重點包含以下兩個主要主題。 （i）基於圍線積分的高度平行和可擴展的特徵值求解器，用於有機多態性和三維光子晶體的數值模擬。 （ii）用於超大規模數據分析的新穎而有效的隨機型奇異值分解。<br> Abstract: We aim at tackling some of the fundamental challenges in matrix computations for large-scale numerical simulation and big data analytics. We intend to develop novel parallel and scalable algorithms to reduce floating-point computation tasks and data communication costs, to implement efficient and robust software packages, and to apply these packages to solve some of the most critical scientific problems. In particular, this subproject will focus on the following two main themes. (i) Highly parallel and scalable eigenvalue solvers based on contour integrals for numerical simulations of organic polymorphism and three-dimensional photonic crystals. (ii) Novel and efficient randomized type singular value decomposition for very large-scale data analysis.高效能計算隨機型奇異值分解圍線積分特徵值求解high-performance computingrandomized singular value decompositioncontour integral