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《Mathematics in Practice and Theory》 2007-01
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Two New Schemes of Newton′s Interation Method Squares Estimator is BLUE

WANG Xia, ZHAO Ling-ling, LI Fei-min(Dept.of Infor.and Cal.Sci,Zhengzhou Inst.of Light Ind,Zhengzhou Henan 450002,China)  
Two new schemes of Newton′s method,which are Simpson Newton′s method and gemetric mean Newton′s method,are developed and their convergence properties are proved.They are at least third order convergence near simple root and one order convergence near multiple roots.In the end,numerical tests are given and compared with other known Newton′s methods.The results show that the proposed methods have some more advantages than others.They enrich the methods to find the roots of non-linear equations and they are important in both theory and application.
【Fund】: 国家自然科学基金(10371111);; 郑州轻工业学院校内基金(2004xjj013)
【CateGory Index】: O242.23
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