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    Please use this identifier to cite or link to this item: http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/41283


    Title: Numerical Schubert Calculus by the Pieri Homotopy Algorithm
    Authors: Li, Tien-yien;Wang, Xiaoshen;吳孟年;Wu, Meng-nien
    Contributors: 淡江大學數學學系
    Keywords: enumerative geometry;Schubert variety;Pieri formula;Pieri homotopy algorithm;Pieri poset
    Date: 2003
    Issue Date: 2010-01-28 07:10:48 (UTC+8)
    Publisher: Philadelphia: Society for Industrial and Applied Mathematics (SIAM)
    Abstract: Based on Pieri's formula on Schubert varieties, the Pieri homotopy algorithm was first proposed by Huber, Sottile, and Sturmfels [J. Symbolic Comput., 26 (1998), pp. 767-788] for numerical Schubert calculus to enumerate all p-planes in Cm+p that meet n given planes in general position. The algorithm has been improved by Huber and Verschelde [SIAM J. Control Optim., 38 (2000), pp. 1265-1287] to be more intuitive and more suitable for computer implementations. A different approach of employing the Pieri homotopy algorithm for numerical Schubert calculus is presented in this paper. A major advantage of our method is that the polynomial equations in the process are all square systems admitting the same number of equations and unknowns. Moreover, the degree of each polynomial equation is always 2, which warrants much better numerical stability when the solutions are being solved. Numerical results for a big variety of examples illustrate that a considerable advance in speed as well as much smaller storage requirements have been achieved by the resulting algorithm.
    Relation: Siam Journal on Numerical Analysis 40(2), pp.578-600
    DOI: 10.1137/S003614290139175X
    Appears in Collections:[Graduate Institute & Department of Mathematics] Journal Article

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