解除方程组中多个变量为一组的线性约束条件的数学处理方法

The mathematical treatment method for relieving the linear constrained conditions with multivariate in equations

本文应用线性空间理论，得出了一种处理含有多个变量的强加边界条件的方法．这种方法广泛应用于含有线性约束条件的变分有限元法及其他变分数值解法，其优点在于处理边界条件时不改变原有的系数矩阵．本文通过对这类数值计算问题的解的唯一性及存在性的讨论，表明了解存在且唯一的一个充分条件是原系数矩阵正定．

A mathematical method of dealing with the imposed boundary conditions with multivariate is presented based upon the linear space theory. It can be applied widely to the finite element method and other numerical variational methods. The merit of this approach is that the main rigid matrix remains unchanged in the process of dealing with the constrained conditions. The sufficient condition of the existance and unigueness of solution is that the original main matrix is positive.