Chaos in Determinant Condensation Calculations

Click to increase image sizeClick to decrease image size

Acknowledgments

The authors sincerely thank to the reviewers and editor for their valuable and detailed comments and suggestions on the early manuscript of this paper, which led to a substantial improvement on the presentation and contents of this paper.

Summary

The phenomenon of chaos plays an important role in real applications. Recently, the Dodgson’s determinant condensation algorithm was revisited in many papers [College Math. Journal 42(1)(2011): 43–54, College Math. Journal 38(2)(2007): 85–95, Math Horizons 14(2)(2006): 12–15,etc.]. This method is attractive, but there also exist some shortcomings. In this paper, a symbolic algorithm and the corresponding problems are discussed to overcome these shortcomings. Numerical experiments show that this symbolic modified algorithm has highly sensitivity on initial configuration of the matrix in condensation process.

Additional information

Notes on contributors

Hou-Biao Li

Hou-Biao Li ([email protected], MR ID 101435, ORCID 0000-0002-7268-307X) received the M.S. and PhD degrees in computational mathematics from the School of Mathematical Science, University of Electronic Science and Technology of China (UESTC), Chengdu, China, in 2004 and 2007, respectively. He is currently a Professor with the School of Mathematical Sciences, UESTC. His research interests are in numerical algebra, scientific computing, mathematical education and artificial intelligence.

Hong Li

Hong Li ([email protected], ORCID 0000-0001-5671-1774) entered China University of Geosciences (CUG) in 1998. She received his BS degree in Mathematics in 2002, spent time as a teacher, then she received the M.S. and Ph.D. degrees in applied mathematics from the School of Mathematical Science, University of Electronic Science and Technology of China (UESTC), Chengdu, China, in 2006 and 2015, respectively. She is currently a Associate Professor with the School of Mathematical Sciences, UESTC. Her research interests are in applied mathematics and dynamical systems.

Ting-Zhu Huang

Ting-Zhu Huang ([email protected], ORCID 0000-0001-7766-230X) received the B.S., M.S., and PhD degrees in computational mathematics from the Department of Mathematics, Xi’an Jiaotong University, Xi’an, China. He is currently a Professor with the School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, China. His current research interests include scientific computation and applications, numerical algorithms for image processing, numerical linear algebra, preconditioning technologies, and matrix analysis with applications.