Approximate eigenvalues, eigenvectors and inverse of a matrix with polynomial entries
Approximate eigenvalues, eigenvectors and inverse of a matrix with polynomial entries
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具有多项式项的矩阵的近似特征值、特征向量和逆矩阵
DOI：
10.1007/bf03167215
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发表时间：
1994
期刊：
影响因子：
--
通讯作者：
T. Kitamoto
中科院分区：
文献类型：
--
作者：
T. Kitamoto
设一个有多项式项的矩阵。本文讨论了以截断幂级数的形式计算m近似的特征值、特征向量和逆。近似特征值的计算是基于幂级数符号求解代数方程的算法。然后，给出了特征向量和逆函数的近似幂级数计算算法。我们为每个算法展示了一个示例。最后，我们解释了幂级数收敛的加速和幂级数截断误差的估计。
LetMbe a matrix with polynomial entries. This paper deals with calculating eigenvalues, eigenvectors and inverse ofMapproximately in the form of truncated power series. The calculation of approximate eigenvalues is based on algorithms solving algebraic equation symbolically in terms of power series. Then, we give algorithms for calculating eigenvectors and inverse in terms of power series approximately. We show an example for each algorithm. Finally, we explain acceleration of convergence of power series and estimate of errors due to truncation of power series.