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Rate of Convergence Proofs of the Method for Finding Roots of Polynomials (Or Eigenvalues of Matrices) by the Power and Inverse Power Methods.

机译：用幂和逆幂方法求多项式（或矩阵特征值）根的方法的收敛性证明。

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Generally known proofs of the convergence of the power method and the inverse power method for finding eigenvalues of a matrix are presented in some detail. The power method is shown to converge geometrically for diagonalizable matrices and proportional to 1/r for nondiagonalizable matrices, where r is the iteration number. The inverse power method is shown to converge at least quadratically for diagonalizable matrices. No rigorous proof of convergence for the inverse power method for nondiagonalizable matrices is given, but several comments are made and an expression for the rate of convergence is presented, along with experimental results. (Author)

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Ehrlich, L. W.;
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年度 1969
页码 1-58
总页数 58
原文格式 PDF
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关键词
Matrix algebra; Numerical analysis; Polynomials; Iterative methods; Convergence; Roots of equations; Eigenvalues;

机译：矩阵代数;数值分析;多项式;迭代法;收敛性;方程根;特征值;

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专利

1. Inverse Power and Durand-Kerner Iterations for Univariate Polynomial Root-Finding [J] . D. A. Bini, L. Gemignani, V. Y. Pan Computers & mathematics with applications . 2004,第2a3期

机译：单变量多项式求根的逆幂和Durand-Kerner迭代
2. Superconvergence two-grid scheme based on shifted-inverse power method for eigenvalue problems by function value recovery [J] . Liu Huipo, Wang Shuanghu, Shen Huayun Computer Methods in Applied Mechanics and Engineering . 2017,第JUNa15期

机译：基于函数值恢复的特征值问题的基于移位逆幂方法的超收敛两网格方案
3. Convergence of Inverse Power Method for First Eigenvalue of p-Laplace Operator [J] . Bozorgnia Farid Numerical Functional Analysis and Optimization . 2016,第10a12期

机译：p-Laplace算子的第一特征值的逆幂方法的收敛性
4. Analytical method of finding polynomial roots by using the eigenvectors, eigenvalues apparatus [C] . Alexander Ivanov, Humbet Aliyev, Bakhyt Bakiyev International Conference on Disaster Recovery and Business Continuity . 2015

机译：使用特征向量，特征向量装置发现多项式根系的分析方法
5. ITERATION MATRICES AND CONVERGENCE RATES OF PROJECTION METHODS. [D] . RIDOLFO, ANTHONY SEATON. 1975

机译：投影方法的迭代矩阵和收敛速度。
6. Discrimination Power of Polynomial-Based Descriptors for Graphs by Using Functional Matrices [O] . Matthias Dehmer, Frank Emmert-Streib, Yongtang Shi, -1

机译：使用函数矩阵的基于多项式的图的判别力
7. A technique to shift an eigenvalue of a complex matrix to accelerate convergence of the power and inverse power method [O] . Bunch K.J., Grow R.W. 1991

机译：移位复杂矩阵特征值以加速幂和逆幂方法收敛的技术

Rate of Convergence Proofs of the Method for Finding Roots of Polynomials (Or Eigenvalues of Matrices) by the Power and Inverse Power Methods.

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