应用非线性隐式迭代法回归含蜡原油触变模型

针对以往含蜡原油触变模型参数回归中实验数据误差被放大和迭代初值不易选取的问题,以非线性参数回归为框架,引入不适定问题的求解思想,应用求解非线性不适定问题的非线性隐式迭代法,一次性回归Houska触变模型的相关参数。对加剂50 mg/kg的中原原油进行参数回归,所得计算值与实验数据吻合较好,最小相对误差为2.71%(26℃),最大相对误差仅为5.09%(21℃)。该方法回归结果准确、稳定,误差随温度的升高而单调减小,可用于求解含蜡原油触变模型参数的回归问题。     

THE THREE-DIMENSIONAL CALCULATING MODEL OF INVERSE PROBLEM IN ECG AND A SPECIAL BOUNDRYVALUE PROBTEM

In this paper, the mathematical model and the three-dimensional finite clement formulation of inverse problem in electrocardiography (ECG) under a general inhomogcneous and anisotropic configuration of the torso conductor is focused on. The following points are especially considered: 1. The mathamatical model is described by a differential equation instead of the Fredholm integral equation. 2. A kind of special boundary value problem is defined as ill-posed boundary value problem. 3. A group of finite element formulation, in which the method that treats anisotropic medium, is built up. 4. The calculating method of ill-posed boundary value problem is discussed.     

具有全局收敛性的非单调不精确牛顿法

对大规模非线性方程组F＝0（其中F：Rn→Rn连续可微）提出2种非单调不精确牛顿法。在算法选代过程中，每步求出F的局部线性化模型的一个近似解，而不要求F的某种范数单调递减，因此具有不精确牛顿法的优点，并且对非常病态的非线性方程组是有效的。在合理假设下证明此算法仍具有全局收敛性。     

Banach空间中的正则Landweber迭代法

利用一致凸一致光滑的Banach空间的几何性质, 研究了Banach空间中线性和非线性算子的正则Landweber迭代法. 假定所测的右端数据具有扰动的情况下, 得出了此正则Landweber迭代法的收敛性.