论文标题
商和特征值问题的梯度
Gradients of Quotients and Eigenvalue Problems
论文作者
论文摘要
交织分析，代数，数值分析和优化，计算现实价值商的共轭共梯度会导致特征值问题。在线性的冬宫案例中，通过检查最佳商，以将共轭共同梯度用于关键点，就会出现广义折叠频谱特征值问题。用$ P $ -NORM替换欧几里得规范，这是所谓的$ p $ -laplacian eigenvalue问题的矩阵版本。这种非线性特征值问题似乎自然被归类为同质问题的特殊情况。作为一个相当一般的阶级，开发了用于恢复给定同质特征值问题是否是梯度特征值问题的工具。事实证明，提出有效的商是一个微妙的问题。提出了一个非线性赫米尔特人特征值问题的概念。引入了Cauchy-Schwarz商。
Intertwining analysis, algebra, numerical analysis and optimization, computing conjugate co-gradients of real-valued quotients gives rise to eigenvalue problems. In the linear Hermitian case, by inspecting optimal quotients in terms of taking the conjugate co-gradient for their critical points, a generalized folded spectrum eigenvalue problem arises. Replacing the Euclidean norm in optimal quotients with the $p$-norm, a matrix version of the so-called $p$-Laplacian eigenvalue problem arises. Such nonlinear eigenvalue problems seem to be naturally classified as being a special case of homogeneous problems. Being a quite general class, tools are developed for recovering whether a given homogeneous eigenvalue problem is a gradient eigenvalue problem. It turns out to be a delicate issue to come up with a valid quotient. A notion of nonlinear Hermitian eigenvalue problem is suggested. Cauchy-Schwarz quotients are introduced.
