Galerkin Eigenvector Approximations
Christopher Beattie
Galerkin 特征向量与试验子空间 中可用的最佳近似值有多接近? 在多种条件下,Galerkin方法给出了一个近似的特征向量,该特征向量不对称地将精确特征向量投射到试验子空间上 - 这比近似特征向量的潜在收敛率更快地发生。 正交Galerkin和Petrov-Galerkin方法都在这里被考虑,特别强调非自体关节问题。 讨论了用有限元方法或光谱方法离散的椭圆PDE的数值处理的后果,并介绍了Krylov子空间方法对大规模矩阵特征值问题的应用。 一对操作符的sep的新下界也被开发出来。
How close are Galerkin eigenvectors to the best approximation available out of the trial subspace ? Under a variety of conditions the Galerkin method gives an approximate eigenvector that approaches asymptotically the projection of the exact eigenvector onto the trial subspace – and this occurs more rapidly than the underlying rate of convergence of the approximate eigenvectors. Both orthogonal-Galerkin and Petrov-Galerkin methods are considered here with a special emphasis on nonselfadjoint pro...