تقرير
A complete pair of solvents of a quadratic matrix pencil
| العنوان: | A complete pair of solvents of a quadratic matrix pencil |
|---|---|
| المؤلفون: | Kurbatov, V. G., Kurbatova, I. V. |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis, Mathematics - Dynamical Systems, Mathematics - Functional Analysis, Mathematics - Spectral Theory, 65F60, 15A69, 46B28, 30E10, 97N50 |
| الوصف: | Let $B$ and $C$ be square complex matrices. The differential equation \begin{equation*} x''(t)+Bx'(t)+Cx(t)=f(t) \end{equation*} is considered. A solvent is a matrix solution $X$ of the equation $X^2+BX+C=\mathbf0$. A pair of solvents $X$ and $Z$ is called complete if the matrix $X-Z$ is invertible. Knowing a complete pair of solvents $X$ and $Z$ allows us to reduce the solution of the initial value problem to the calculation of two matrix exponentials $e^{Xt}$ and $e^{Zt}$. The problem of finding a complete pair $X$ and $Z$, which leads to small rounding errors in solving the differential equation, is discussed. Comment: 24 pages, 16 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2405.07210 |
| رقم الأكسشن: | edsarx.2405.07210 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |