Robust numerical methods for nonlinear equations

2006年，首席研究员在国际期刊上发表了3篇论文。研究人员不仅致力于数学研究，还研究了数值方法在解决许多现实世界问题中的应用。在赠款的支持下，研究人员参加了几次国际会议，并在会议上展示了他们的研究成果。此外，他们还与世界一流的研究人员交流了他们的新研究成果。主要结果如下：1.首席研究者将球面t-设计转化为欠定非线性方程，并与新南威尔士大学的Robert Woersley教授一起证明了球面t-设计的存在性。2.与Hirosaki大学的T.Kimura(Hirosaki大学博士生)提出了一种新的用于桥梁管理的有限元曲面拟合方法。我们使用KITACON公司的方法和数据分析了青森地区桥梁损坏的因素。3.首席研究员与中南大学的项士祥教授一起给出了线性互补问题的新误差界。新的误差界极大地改善了现有的误差界。此外，对于一些特殊的线性互补问题，包括H-矩阵的线性互补问题，它们也很容易计算。我们从这些领域的专家那里得到了非常积极的评价。

During 2006,the head investigator published 3 papers in international journals. The investigators have not only worked on mathematics but also studied applications of numerical methods for solving many real world problems. By the support of the grants, investigators have attended several international conferences and presented their research results in the conferences. Moreover, they exchanged their new research results with world class researchers. Some established results are summarized as the follows.1.The head investigator reformulated the spherical t-design to underdetermined nonlinear equations and proved the existence of spherical t-designs with Prof. Robert Womersley of the University of New South Wales. We also applied the Guass-Newton method to find approximate spherical t-design and defined new numerical integration rules on the sphere.2.The head investigator proposed a new finite element surface fitting method for bridge management with T.Kimura of Hirosaki University ( current Ph. D student in Hirosaki University). We used the method and date from KITACON company to analyze the factors which damage the bridges in Aomori region.3.The head investigator gave new error bounds for linear complementarity problems with Prof. S.Xiang of South Center University. The new error bounds improved existing error bounds greatly. Moreover, they can be computed easily for some special linear complementarity problems including H-matrix linear complementarity problems. We received very positive comments from experts in the areas.