A Riemannian Newton Algorithm for Nonlinear Eigenvalue Problems
A Riemannian Newton Algorithm for Nonlinear Eigenvalue Problems
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DOI：
10.1137/140967994
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发表时间：
2015-06
期刊：
影响因子：
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通讯作者：
Zhi Zhao;Zhengjian Bai;X. Jin
中科院分区：
文献类型：
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作者：
Zhi Zhao;Zhengjian Bai;X. Jin
我们给出了黎曼牛顿算法的公式，用于通过最小化受正交性约束的总能量函数来解决一类非线性特征值问题。在一些温和的假设下，我们建立了所提出方法的全局和二次收敛性。此外，还推导了总能量函数在解处的黎曼Hessian矩阵的正定性条件。一些数值测试被报道来说明所提出的方法解决大规模问题的效率。
We give the formulation of a Riemannian Newton algorithm for solving a class of nonlinear eigenvalue problems by minimizing a total energy function subject to the orthogonality constraint. Under some mild assumptions, we establish the global and quadratic convergence of the proposed method. Moreover, the positive definiteness condition of the Riemannian Hessian of the total energy function at a solution is derived. Some numerical tests are reported to illustrate the efficiency of the proposed method for solving large-scale problems.