强单调对称非线性方程组的BFGS算法

提出一种求解强单调非线性方程组的BFGS算法，该算法的一个明显优点是Bκ的条件数比Li-Fukushima^3]提出的GNBFGS中Bκ的条件数小得多。且该算法是一种无需计算导数的下降算法。在一定的条件下，证明了算法的全局收敛性和超线性收敛性。最后进行数值试验，结果表明，本文算法具有较好的数值结果。而且验证了本文所提出的算法中Bκ的条件数要比GNBFGS算法的条件数小得多。

A BFGS METHOD FOR SOLVING STRONGLY MONOTONE SYMMETRIC NONLINEAR EQUATIONS

We presented a BFGS method for solving strongly monotone symmetric nonlinear equations. Compared with Guass-Newton BFGS method（GNBFGS） proposed by Li-Fukushima （2001） for solving sym metric nonlinear equations, the condition number of Bκ in our methods is much less than that of Guass-Newton BFGS method. The method is a descent method without extra computation of derivative. Under appropriate conditions, we show that the method is globally and super linearly convergent. Finally , a numeric test has been done. Our numerical results show that the proposed BFGS methods have a better numerical result and also prove that the condition number in this paper is much smaller than that in GNBFGS.