CONVERGENCE ANALYSIS OF PROJECTION METHODS FOR THE NUMERICAL SOLUTION OF LARGE LYAPUNOV EQUATIONS

Simoncini V; Druskin V

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CONVERGENCE ANALYSIS OF PROJECTION METHODS FOR THE NUMERICAL SOLUTION OF LARGE LYAPUNOV EQUATIONS

机译：大Lyapunov方程数值解的投影方法的收敛性分析

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The numerical solution of large-scale continuous-time Lyapunov matrix equations is of great importance in many application areas. Assuming that the coefficient matrix is positive definite, but not necessarily symmetric, in this paper we analyze the convergence of projection-type methods for approximating the solution matrix. Under suitable hypotheses on the coefficient matrix, we provide new asymptotic estimates for the error matrix when a Galerkin method is used in a Krylov subspace. Numerical experiments confirm the good behavior of our upper bounds when linear convergence of the solver is observed.

机译：大规模连续时间Lyapunov矩阵方程的数值解在许多应用领域中具有重要意义。假设系数矩阵是正定的，但不一定是对称的，在本文中，我们分析了逼近解矩阵的投影型方法的收敛性。在系数矩阵的适当假设下，当在Krylov子空间中使用Galerkin方法时，我们为误差矩阵提供了新的渐近估计。当观察到求解器的线性收敛时，数值实验证实了我们上限的良好行为。

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《SIAM Journal on Numerical Analysis》 |2010年第2期|共16页
作者
Simoncini V; Druskin V;
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原文格式 PDF
正文语种 eng
中图分类数值分析;
关键词
Lyapunov equation; Krylov subspace; matrix exponential; Faberpolynomials;

机译：Lyapunov方程;Krylov子空间;矩阵指数;Faber多项式;

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专利

1. CONVERGENCE ANALYSIS OF PROJECTION METHODS FOR THE NUMERICAL SOLUTION OF LARGE LYAPUNOV EQUATIONS [J] . Simoncini V, Druskin V SIAM Journal on Numerical Analysis . 2010,第2期

机译：大Lyapunov方程数值解的投影方法的收敛性分析
2. Numerical solution of nonlinear Volterra-Fredholm-Hammerstein integral equations via Tau-collocation method with convergence analysis [J] . Gouyandeh Z., Allahviranloo T., Armand A. Journal of Computational and Applied Mathematics . 2016,第Null期

机译：基于Tau配点法的非线性Volterra-Fredholm-Hammerstein积分方程的数值解及其收敛性分析。
3. Numerical Solution for a Class of Linear System of Fractional Differential Equations by the Haar Wavelet Method and the Convergence Analysis [J] . Yiming Chen, Xiaoning Han, Lechun Liu Computer Modeling in Engineering & Sciences . 2014,第5期

机译：一类分数阶微分方程线性系统的Haar小波方法和收敛性分析
4. Solution of Fractional Order Differential Equation by the Haar Wavelet Method. Numerical Convergence Analysis for Most Commonly Used Approach [C] . Majak J., Shvartsman B., Pohlak M., International Conference of Numerical Analysis and Applied Mathematics . 2016

机译：哈尔小波法的分数级微分方程解。最常用方法的数值收敛分析
5. CONVERGENCE AND SUPERCONVERGENCE OF NUMERICAL SOLUTIONS OF WEAKLY SINGULAR INTEGRAL AND DIFFERENTIAL EQUATIONS (GALERKIN, COLLOCATION, EIGENVALUES, EIGENVECTORS, SPLINES) [D] . LEBBAR, RACHID. 1986

机译：弱奇异积分和微分方程数值解的收敛性和超级度验收（Galerkin，Collocation，特征值，特征向量，花键）
6. Convergence Analysis and Numerical Study of a Fixed-Point Iterative Method for Solving Systems of Nonlinear Equations [O] . Na Huang, Changfeng Ma -1

机译：求解非线性方程组的不动点迭代法的收敛性分析和数值研究
7. An extension of the spectral Tau method for numerical solution of multi-order fractional differential equations with convergence analysis [O] . Ghoreishi F., Yazdani S. 2011

机译：频谱Tau法扩展的具有收敛性的多阶分数阶微分方程数值解。
8. A Projection Method for the Numerical Solution of a System of First-Order Nonlinear Differential Equations with Mixed Boundary Conditions. [R] . van schieveen, hendrik m. 1975

机译：具有混合边界条件的一阶非线性微分方程组数值解的投影方法。

CONVERGENCE ANALYSIS OF PROJECTION METHODS FOR THE NUMERICAL SOLUTION OF LARGE LYAPUNOV EQUATIONS

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