澳大教授在世界華人數學家大會發表報告

金小慶(左)出席世界華人數學家大會

孫海衛

Two professors from the University of Macau's (UM) Department of Mathematics, namely Distinguished Professor Jin Xiaoqing and Full Professor Sun Haiwei, recently attended the Eighth International Congress of Chinese Mathematicians (ICCM 2019) held at Tsinghua University in Beijing. Both professors gave a 45-minute academic report. Prof Jin was also invited to serve as a member of the Executive Committee of the conference.

Initiated in 1998 by the world-renowned mathematician Prof Shing-Tung Yau, the ICCM is a triennial event that brings together Chinese and overseas mathematicians to discuss the latest developments and future directions in both pure and applied mathematics. It is the largest and most influential maths conference in the world.

At the conference, Prof Jin gave a presentation titled ‘A Brief Survey of Matrix Manifold Computation’. He discussed the nonnegative inverse eigenvalue problem, and reformulated the problem as an underdetermined constrained nonlinear matrix equation over several matrix manifolds. He then proposed a Riemannian inexact Newton-CG method for solving the nonlinear matrix equation. Under some mild assumptions, he established the global and quadratic convergence of the proposed method. Prof Sun gave a presentation titled ‘Fast Algorithms for Numerical Solutions of Fractional Partial Differential Equations’. He discretised the fractional partial differential equation by the implicit finite difference scheme with the shifted Grunwald formula. The scheme is unconditionally stable and the coefficient matrix possesses a Toeplitz-like structure. He then explained several fast iterative methods for solving the resulting systems. He also discussed how the fast Toeplitz matrix-vector multiplication is utilised to lower the computational cost with only O(N log N) complexity, where N is the number of grid points.

The research team in computational mathematics, led by Prof Jin, has achieved impressive results in the past decade. Team members have received two second prizes of the Natural Science Award from the Macao SAR government. Graduates from the department have also won numerous awards.

澳門大學科技學院數學系特聘教授金小慶和教授孫海衛應邀出席於北京清華大學召開的第八屆世界華人數學家大會，並作45分鐘學術報告；此外，金小慶還被邀請為大會的執行委員會成員。該大會是國際華人數學界規模最大、最具影響力的頂級學術盛會。

世界華人數學家大會由國際數學大師丘成桐教授於1998年發起設立，其使命是加強海內外華人數學家的聯繫，研討數學科學國際最新研究進展，促進中國數學和世界數學科學共同發展，而大會的執行委員會成員更是來自世界各地的著名數學家。

會上，金小慶以“矩陣梳形計算之簡要綜述”為題，介紹了非負矩陣特徵值反問題以及電子結構計算中一類特殊非線性特徵值問題。針對兩類問題，他分別提出兩類不同的非精確黎曼牛頓型演算法。在一定假設條件下，兩類方法均具有全局以及局部二次收斂的特性。孫海衛則以“分數階偏微分方程數值解的快速方法”為題，利用隱式格式結合帶位移的GL公式去離散分數階偏微分方程，這一離散格式無條件穩定，並且其系數矩陣具有擬托普利茲結構。他還介紹了幾類快速反覆運算法求解離散後的線性系統。其中，利用快速傅立葉變換，托普利茲矩陣乘以向量的計算量可以降低到N log N的數量級，這裡N是格點的個數。

澳大科技學院數學系以金小慶為首的計算數學團隊，在近十年裏取得很大成就。團隊成員曾獲澳門特區政府頒發的自然科學二等獎兩次，分別是金小慶、黃錫榮和鄭智文（2016）以及孫海衛和李兆隆（2018）。同時培養了許多優秀的研究生，包括林學磊（新世界數學獎銀獎、EASIAM二等獎、澳門政府優秀研究生科研獎）、趙志（EASIAM一等獎）、呂品（EASIAM二等獎、澳門政府優秀研究生科研獎）等。澳大計算數學團隊已經在國際計算數學界佔有重要的一席之地。