Robust numerical methods for nonlinear equations

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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.