We present a new approach to compute eigenvalues and eigenvectors of locally definite multiparameter eigenvalue problems by its signed multiindex. The method has the interpretation of a semismooth Newton method applied to certain functions that have a unique zero. We can therefore show local quadratic convergence, and for certain extreme eigenvalues even global linear convergence of the method. Local definiteness is a weaker condition than right and left definiteness, which is often considered for multiparameter eigenvalue problems. These conditions are naturally satisfied for multiparameter Sturm-Liouville problems that arise when separation of variables can be applied to multidimensional boundary eigenvalue problems.

翻译：我们提出了一种新方法，通过符号多指标计算局部确定多参数特征值问题的特征值与特征向量。该方法可解释为对具有唯一零点的特定函数应用半光滑牛顿法。因此，我们能够证明该方法的局部二次收敛性，并且对于某些极端特征值，甚至能证明全局线性收敛性。局部确定性是比通常多参数特征值问题中考虑的右确定性与左确定性更弱的条件。当多维边界特征值问题可应用变量分离法时，这些条件自然满足于由此产生的多参数Sturm-Liouville问题。