肺磁场中弛豫曲线拟合的一个方法——非线性最小二乘问题的PSB算法

A METHOD OF RELAXATION CURVE FITTING IN THE MAGNETIC FIELD PRODUCED BY THE LUNG——AN ALGORITHM OF THE POWELL SYMMETRIC BROYDEN UPDATE FOR SOLVING THE NONLINEAR LEAST-SQUARE PROBLEM

§1.问题的提出 尘肺是危害最大的一类职业病。目前对尘肺的诊断主要依靠X线摄片,当胸片已能看出病变时,对治疗已为时过晚。1973年Cohen作出第一张人体肺磁图后,立即引起各国学者的关注。因为磁测量的方法比超声波和X射线分析的灵敏度要高好几个数量级。这将为尘肺的早期诊断开辟了道路,也有助于对作业环境粉尘卫生标准的制定。

In this paper, we give a method of relaxation curve fitting in the magneticfield produced by the lung. this method is developed for solving the nonlinear least-squares problem. An estimate for the second derivative of Q(x)=f(x)~Tf(x) is con-structed as the sum of two matrices. The first matrix is the usual first-order estim-ate used by the Gauss method while the second matrix is generated recursively usingthe symmetric secant update of Powell. Test results indicate that the method is su-perior to the Gauss-Newton type methods.