一类特殊的三对角矩阵特征值的计算及应用

The computation of eigenvalue for a special class of tridiagonal matrix and its applications

研究一种特殊的三对角矩阵特征值的计算及其在偏微分方程数值解中的应用.通过用求解带有不同边界条件的差分方程的办法来求解特殊三对角矩阵的特征值,并将三对角矩阵的特殊性归结为边界条件的不同,由此给出三对角矩阵特征值的计算公式,并研究其在偏微分方程数值解数值格式稳定性中的应用.

In this article, the computation of eigenvalue for a special class of tridiagonal matrix is discussed, and its applications to the stability of numerical schemes in numerical partial differential equations are studied. Firstly, the eigenvalue of special tridiagonal matrix is computed through solving difference equation with different boundary con- ditions. By converting the difference of matrix into difference of boundary conditions, the analytic formulation of ei- genvalues for the tridiagonal matrix is generated. Finally, some simple applications in numerical partial differential equations are given.