论文标题
具有梯度方法应用的同质雷利商
A homogeneous Rayleigh quotient with applications in gradient methods
论文作者
论文摘要
鉴于近似特征向量，其（标准）瑞利商和谐波雷利商是相应特征值的两个众所周知的近似值。我们提出了一种新型的瑞利商，同质的雷利商，并分析了其对特征向量扰动的敏感性。此外，我们研究了这种均匀的雷利商的倒数，它是无约束优化的梯度方法的步骤。概念和基本属性也扩展到广义特征值问题。
Given an approximate eigenvector, its (standard) Rayleigh quotient and harmonic Rayleigh quotient are two well-known approximations of the corresponding eigenvalue. We propose a new type of Rayleigh quotient, the homogeneous Rayleigh quotient, and analyze its sensitivity with respect to perturbations in the eigenvector. Furthermore, we study the inverse of this homogeneous Rayleigh quotient as stepsize for the gradient method for unconstrained optimization. The notion and basic properties are also extended to the generalized eigenvalue problem.
