论文标题
单调非线性特征向量问题的变分表征和自洽场迭代的几何形状
Variational Characterization of Monotone Nonlinear Eigenvector Problems and Geometry of Self-Consistent-Field Iteration
论文作者
论文摘要
本文涉及一类单调特征值非线性问题（MNEPV）。 MNEPV在应用中遇到了诸如矩阵的关节数值半径，三阶部分对称张量的最佳级别近似值，以及耗散性汉密尔顿差异差异代数方程的距离。我们首先提出MNEPV的变异表征。基于变分的特征，我们提供了用于求解MNEPV，证明SCF的全局收敛并设计加速SCF的自洽场（SCF）迭代的几何解释。来自多种应用的数值示例证明了SCF及其加速度的理论属性和计算效率。
This paper concerns a class of monotone eigenvalue problems with eigenvector nonlinearities (mNEPv). The mNEPv is encountered in applications such as the computation of joint numerical radius of matrices, best rank-one approximation of third-order partial symmetric tensors, and distance to singularity for dissipative Hamiltonian differential-algebraic equations. We first present a variational characterization of the mNEPv. Based on the variational characterization, we provide a geometric interpretation of the self-consistent-field (SCF) iterations for solving the mNEPv, prove the global convergence of the SCF, and devise an accelerated SCF. Numerical examples from a variety of applications demonstrate the theoretical properties and computational efficiency of the SCF and its acceleration.
