The local convergence of alternating optimization methods with overrelaxation for low-rank matrix and tensor problems is established. The analysis is based on the linearization of the method which takes the form of an SOR iteration for a positive semidefinite Hessian and can be studied in the corresponding quotient geometry of equivalent low-rank representations. In the matrix case, the optimal relaxation parameter for accelerating the local convergence can be determined from the convergence rate of the standard method. This result relies on a version of Young's SOR theorem for positive semidefinite $2 \times 2$ block systems.

翻译：确定交替优化方法与低级矩阵和高压问题过度松绑的局部趋同; 分析基于这种方法的线性化,其形式是正半无底黑森的SOR迭代,可以对等的低级表示法进行相应的商数几何研究; 在矩阵中,可以通过标准方法的趋同率确定加速地方趋同的最佳放松参数。 其结果依赖于正半无底化半无底化的SOR定理系统版本 2\乘以2美元区块系统。