Successive Partial-Symmetric Rank-One Algorithms for Almost Unitarily Decomposable Conjugate Partial-Symmetric Tensors

In this paper,we introduce the almost unitarily decomposable conjugate partial-symmetric tensors,which are different from the commonly studied orthogonally decomposable tensors by involving the conjugate terms in the decomposition and the perturbation term.We not only show that successive rank-one approximation algorithm exactly recovers the unitary decomposition of the unitarily decomposable conjugate partial-symmetric tensors.The perturbation analysis of successive rank-one approximation algorithm for almost unitarily decomposable conjugate partial-symmetric tensors is also provided to demonstrate the robustness of the algorithm.

Global Complexity Bound of the Inexact Levenberg–Marquardt Method

In this paper,we investigate the global complexity bound for the inexact Levenberg–Marquardt method,where the Jacobian may be perturbed and the solution is possibly not exact.Under reasonable assumptions,we show that the global complexity bound is O(ε^(−2)),which is the same as the exact case.We also show that it can be reduced to O(lgε^(−1))under some regularity assumption.