论文标题
riemannian歧管上非线性方程的光谱残差方法
Spectral Residual Method for Nonlinear Equations on Riemannian Manifolds
论文作者
论文摘要
在本文中，非线性方程（SANE）的光谱算法适应了在riemannian歧管上找到给定切线矢量场的零的问题。 SANE的广义版本以系统的方式将切线向量字段用作搜索方向和连续的实现函数，该函数适应了此方向并确保其验证相关的功绩函数的下降条件。为了加快所提出方法的收敛性，我们将Riemannian自适应光谱参数与非符号酮全球化技术结合在一起。拟议程序的全球融合是根据某些标准假设建立的。数值结果表明，我们的算法在不同的riemannian歧管上非常有效地解决切线矢量场，并与最近发布的Polak-ribiére-Polyak方法和文献中存在的其他方法相竞争。
In this paper, the spectral algorithm for nonlinear equations (SANE) is adapted to the problem of finding a zero of a given tangent vector field on a Riemannian manifold. The generalized version of SANE uses, in a systematic way, the tangent vector field as a search direction and a continuous real-valued function that adapts this direction and ensures that it verifies a descent condition for an associated merit function. In order to speed up the convergence of the proposed method, we incorporate a Riemannian adaptive spectral parameter in combination with a non-monotone globalization technique. The global convergence of the proposed procedure is established under some standard assumptions. Numerical results indicate that our algorithm is very effective and efficient solving tangent vector field on different Riemannian manifolds and competes favorably with a Polak-Ribiére-Polyak Method recently published and other methods existing in the literature.
