Eigenvalue Problems
Eigenvalue Problems
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DOI：
10.2307/j.ctvcm4h3p.17
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发表时间：
2021-01
期刊：
影响因子：
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通讯作者：
Morten Hjorth-Jensen
中科院分区：
文献类型：
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作者：
Morten Hjorth-Jensen
在自然科学和工程学中，经常使用微分方程和微分方程组。他们的解决方案导致了特征值问题。因此，特征值问题在线性代数中占有重要地位。在本标题中，我们将考虑特征值问题以及特征值的线性和二次问题。在研究特征值线性问题时，我们重点关注非对称情况下的QR算法和对称情况下的最小最大表征。在研究特征值的二次问题时，我们考虑线性化和变分表征。我们用实际例子来说明一切。其他只是一些特征值。首先确定特征多项式的系数，然后确定特征值的方法
In natural sciences and engineering, are often used differential equations and systems of differential equations. Their solution leads to the problem of eigenvalues. Because of that, problem of eigenvalues occupies an important place in linear algebra. In this caption we will consider the problem of eigenvalues, and to linear and quadratic problems of eigenvalues. During the studying of linear problem of eigenvalues, we put emphasis on QR algorithm for unsymmetrical case and on minmax characterization of symmetric case. During the studying of quadratic problems of eingenvalue, we consider the lineariza‐ tion and variational characterization. We illustrate all with practical examples. and the other just a few of the eigenvalues. Methods based on first determining the coefficients of the characteristic polynomial, and later to determining the eigenvalue