Yunfeng Cai

Research Fellow

Personal Profile

I am now a research fellow at DESC, School of Mathematical Sciences, Peking Uinv., P.R. China.
From Jan. 2010 to Jul. 2012, I was a postdoc at Dept. of CS, UC Davis, US.
During 2009, I was a postdoc in Institute of Mathematics, Chinese Academy of Sciences.
I revceived my PHD degree from Peking Univ. in Jan, 2009.

Research Interest

large scale eigenvalue problem with applications in electronic structure calculations, inverse eigenvalue problems, tensor decomposition, etc.

Teaching Courses

Numerical Linear Algebra II

Sep., 2016, Sep., 2015,Sep. 2014, Sep. 2013, Sep. 2012

graduate students and undergraduate students from Math.

Advanced Mathematics B/C

Feb. 2015, Feb. 2014, Feb. 2013

undergradute students from Medicine, Physics, Guanghua Management.


Y.F. Cai, C.Y. Liu, An Algebraic Approach to Nonorthogonal General Joint Block Diagonalization , SIAM J. on Matrix Analysis and Applications, Vol. 38, pp. 50--71, 2017.

Z.C. Guo, J. Qian, Y.F. Cai, S.F. Xu, Refined Schur Method for Robust Pole Assignment with Repeated Poles , IEEE Transactions on Automatica Control, Vol. 61, Issue 9, pp. 2370 - 2385, 2016.

H. Li, Y.F. Cai, Solving the real eigenvalues of Hermitian quadratic eigenvalue problems via bisection, Electronic Journal of Linear Algebra, Vol. 30, pp. 721--743, 2015.

H. Li, Y.F. Cai, A Jacobi-Davidson type method for computing real eigenvalues of the quadratic eigenvalue problem, Calcolo, pp. 1--13, 2015.

Y.F. Cai, D.C. Shi, S.F. Xu, A matrix polynomial spectral approach for general joint block diagonalization , SIAM J. on Matrix Analysis and Applications, Vol. 36, pp. 839--863, 2015.

D.C. Shi, Y. F. Cai, S.F. Xu, Some perturbation results for a normalized Non-Orthogonal Joint Diagonalization problem, Linear Algebra and its Applications, Vol. 484, pp. 457--476, 2015.

P.C. Guo, Y.F. Cai, J. Qian, S.F. Xu, Perturbation analysis of the extinction probability of a Markovian binary tree , Linear Algebra and its Applications, Vol. 475, pp. 11--27, 2015.

Z.C. Guo, Y.F. Cai, J. Qian, S.F. Xu, A modified Schur method for robust pole assignment in state feedback control , Automatica, Vol. 52, pp. 334--339, 2015.

Y.F. Cai, Z. Bai, J. E. Pask, N. Sukumar, Hybrid preconditioning for iterative diagonalization of ill-conditioned generalized eigenvalue problems in electronic structure calculations , Journal of Computational Physics, Vol. 255, pp. 16--30, 2013.

Y.F. Cai, J. Qian and S.F. Xu, Robust partial pole assignment problem for high order control systems, Automatica, Vol. 48, pp. 1462--1466, 2012.

Y.F. Cai, J. Qian and S.F. Xu, The Formulation and Numerical Method for Partial Quadratic Eigenvalue Assignment Problems, Numerical Linear Algebra with Applications, Vol. 18, pp. 637--654, 2011.

Y.F. Cai and S.F. Xu, A New Eigenvalue Embedding Approach for Finite Element Model Updating, Taiwanese Journal of Mathematics, Vol.14, No. 3A, pp. 911--932, 2010.

Y.F. Cai and S.F. Xu, On a quadratic inverse eigenvalue problem, Inverse Problems, Vol.25, No. 8, 085004, doi: 10.1088/0266-5611/25/8/085004, 2009.

Y.F. Cai, Y.C. Kuo, W.W. Lin and S.F. Xu, Solutions to a quadratic inverse eigenvalue problem, Linear Algebra and Its Applications, Vol.430, No. 5-6, pp. 1590--1606, 2009.


Tensor Decomposition


Education Background

Peking University

Sep. 2004 ~ Jan. 2009

PHD in Computing Mathematics.

University of Science and Technology of China

Sep. 2000 ~ Jul. 2004

Bachlor degree in Mathematics.

Useful Links

Last updated in Dec., 2015.