Convergence rates and explicit error bounds of Hill's method for spectra of self-Adjoint differential operators
Convergence rates and explicit error bounds of Hill's method for spectra of self-Adjoint differential operators
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自伴随微分算子谱的 Hill 方法的收敛率和显式误差界
DOI：
10.1007/s13160-013-0125-1
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发表时间：
2014
影响因子：
0.9
通讯作者：
Sunao Murashige
中科院分区：
文献类型：
--
作者：
Ken'ichiro Tanaka;Sunao Murashige
给出了计算周期系数常微分算子谱的数值方法Hill方法的收敛速度和显式误差界。该方法通过一个有限维矩阵来逼近算子。在自伴算子的假设下，证明了在一定条件下，特征值关于维数的收敛速度和显式的误差界.数值算例表明，对于某些真实的问题，我们可以利用Gershgorin定理来验证这些条件.主要定理证明使用邓福德积分投影向量到一个特定的特征空间。
We present the convergence rates and the explicit error bounds of Hill’s method, which is a numerical method for computing the spectra of ordinary differential operators with periodic coefficients. This method approximates the operator by a finite dimensional matrix. On the assumption that the operator is self-adjoint, it is shown that, under some conditions, we can obtain the convergence rates of eigenvalues with respect to the dimension and the explicit error bounds. Numerical examples demonstrate that we can verify these conditions using Gershgorin’s theorem for some real problems. Main theorems are proved using the Dunford integrals which project an vector to a specific eigenspace.