论文标题
使用交替方法解决两参数特征值问题
Solving two-parameter eigenvalue problems using an alternating method
论文作者
论文摘要
我们提出了一种新的方法来计算两参数征值问题的选定特征值和特征向量。我们的方法需要计算与初始两参数特征值问题的矩阵相同大小的广义特征值问题。该方法适用于正确的确定问题，可能是在执行仿射转换后。当应用变量分离时，这包括一类Helmholtz方程。我们为极端特征值和经验证据提供了融合证明，并为其他特征值提供了局部融合证明。
We present a new approach to compute selected eigenvalues and eigenvectors of the two-parameter eigenvalue problem. Our method requires computing generalized eigenvalue problems of the same size as the matrices of the initial two-parameter eigenvalue problem. The method is applicable for right definite problems, possibly after performing an affine transformation. This includes a class of Helmholtz equations when separation of variables is applied. We provide a convergence proof for extremal eigenvalues and empirical evidence along with a local convergence proof for other eigenvalues.
