Frontiers of Mathematics in China >

2015 , Vol. 10 >Issue 1: 221 - 237

DOI: https://doi.org/10.1007/s11464-014-0417-z

RESEARCH ARTICLE

Effective algorithms for computing triangular operator in Schubert calculus

  • Kai ZHANG , 1 ,
  • Jiachuan ZHANG 1 ,
  • Haibao DUAN 2 ,
  • Jingzhi LI , 3
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  • 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

Received date: 01 Jun 2014

Accepted date: 18 Jul 2014

Published date: 30 Dec 2014

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

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.

Key words： Triangular operator; Schubert calculus; parallel algorithm; central binomial coefficient

Cite this article

Kai ZHANG , Jiachuan ZHANG , Haibao DUAN , Jingzhi LI . Effective algorithms for computing triangular operator in Schubert calculus[J]. Frontiers of Mathematics in China, 2015 , 10(1) : 221 -237 . DOI: 10.1007/s11464-014-0417-z

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