Effective algorithms for computing triangular operator in Schubert calculus  

作　　者：Kai ZHANG Jiachuan ZHANG Haibao DUAN Jingzhi LI 

机构地区：[1]Department of Mathematics, Jilin University, Changchun 130023, China [2]Institute of Mathematics, Chinese Academy of Sciences, Beijing 100080, China [3]Faculty of Science, South University of Science and Technology of China, Shenzhen 518055,China

出　　处：《Frontiers of Mathematics in China》2015年第1期221-237,共17页中国高等学校学术文摘·数学（英文）

基　　金：The authors sincerely appreciate the referees for acknowledging the manuscript and providing valuable comments and suggestions that benefit their manuscript. This work was supported by the National Natural Science Foundation of China （Grant Nos. 11131008, 11271157, 11201453, 11471141）, the 973 Program （2011CB302400）, the Open Project Program of the State Key Lab of CAD＆CG （A1302） of Zhejiang University, and the Scientific Research Foundation for Returned Scholars, Ministry of Education of China. They also wish to thank the High Performance Computing Center of Jilin University and Computing Center of Jilin Province for essential computing support.

摘　　要：We develop two parallel algorithms progressively based on C＋＋ to compute a triangle operator problem, which plays an important role in the study of Schubert calculus. We also analyse the computational complexity of each algorithm by using combinatorial quantities, such as the Catalan number, the Motzkin number, and the central binomial coefficients. The accuracy and efficiency of our algorithms have been justified by numerical experiments.We develop two parallel algorithms progressively based on C＋＋ to compute a triangle operator problem, which plays an important role in the study of Schubert calculus. We also analyse the computational complexity of each algorithm by using combinatorial quantities, such as the Catalan number, the Motzkin number, and the central binomial coefficients. The accuracy and efficiency of our algorithms have been justified by numerical experiments.

关 键 词：Triangular operator Schubert calculus parallel algorithm centralbinomial coemcient 

分 类 号：O123.1[理学—数学] TP301.6[理学—基础数学]