Academician Chen Mufa Discusses Crossover Research

On October 25th, Professor Chen Mufa, an academician of the Chinese Academy of Sciences was invited to Tianjin University and shared his experience and understanding of crossover research in a leture with young scholars and students from the School of Mathematics.

Academician Chen is engaged in the field of probability theory, mathematical physics, differential geometry and random process classification. In recent years, he developed a keen interest in the calculation of matrices eigenvalues , and based on his research results in probability theory, he has found a way to improve the accuracy and efficiency of the calculations and their corresponding eigenvectors.

During the lecture, Chen reviewed his mathematical research based on his research experience and background in different periods. From the promotion and application of optimum, seeking methods to production practices in the 1970s, to the research on economic optimization in the late 1980s, and then to the research on numerical mathematics in the past four years, he described himself as a “vagrant”.

Chen explained the concept of Hermtizable matrices and related theories. In 2018, he presented an equivalent criterion of Hermtizable matrix. In particular, he pointed out that for the tridiagonal matrix, this criterion can be further specified, which can be used to describe the birth and death of specie.

He also discussed the algorithm of the eigenvalues and eigenvectors of matrices. From the perspective of calculation, it is easy to calculate in the case of symmetry, but not in the case of asymmetry. In order to solve these problems, he proposed using a coupling method, which greatly improves the calculating speed and accuracy. He found that these "improved general algorithms" can be applied to more general matrices, and yield many satisfactory results in many important cases.

Chen also talked about how he views multidisciplinary study for scholars. He believed that all disciplines were connected and that knowledge about one discipline might enlighten ones’s research in other disciplines. “As a researcher, we should learn to think creatively to solve the substantive problems in the fields we cross”, Chen reflected.

By the School of Mathematics

Editors: Eva Yin & Doris Harrington