利用非线性方程组求解矩阵特征值特征向量

矩阵特征值问题已成为数值计算中的一个重要组成部分 ,为有效求解此类问题 ,提出了一种求解特征值的新方法 :利用非线性方程组的Newton迭代法求解特征向量 ,为提高迭代的收敛速度 ,引入同伦思想 ,利用插值方法 ,得到近似特征向量Y(N) ,以Y(N) 作为迭代初值 ,从而快速求出问题的具有较高精度的解 .该算法稳定性好 ,可并行运算

A new algorithm for computing the eigenpairs of a matrix by Newton iteration

Matrix's eigenvalue problem,concerned with morden computational physic computational chemics,computational biology,many scientific research and engineer computation, hasbeen a main component of Numerial computation.This paper works on solving the problem effectively.It presents a new method of computing eigenpairs by Newton iterationfor nonlinear equations.In order to improve iteration convergence rate,it introduces a homotopy idea,and employs interpolation to attain approximate eigenvector Y (N).As a result,we can get more accurate solution rapidly when employing Y (N) as an iteration starting value.The paper includes some discussion about algorithm stability. The algorithm has the advantage of parallel working.