## Shanks变换及其应用+文献综述

Shanks Transformation and its Application
Abstract
The iterative method of linear algebraic equations is an extreme method is an effective method for the solution of large sparse matrix equation    s. The basic idea is to a certain limit process to gradually approach the exact solution of linear equations, a step-by-step approximation method. The iterative method will be iterative formula for a deformation of n linear equations. For any given iteration of the initial value, by an iterative scheme can generate a vector sequence, our aim is the solution to solving the equations, so we will want to limit approximation the solution of equations of vector sequences.
This paper introduced the definition and form of the Shanks Transformation, The iterative method of linear equations is discussed and analysed by using Shanks Transformation. The pergent iterative sequence is changed into a convergent one under some conditions, and accelerated the solutions. The application of the Shanks Transformation in the acceleration of the solution of the series has been studied.
Key words: linear equations, series, iteration, acceleration, convergence, Shanks Transformation

1    Shanks变换介绍    1
1.1    Shanks变换简介    1
1.2    Shanks变换举例    1
1.3    Shanks变换推导    2
2    Shanks变换的应用    3
2.1    Shanks变换在线性方程组迭代解法的收敛与加速中的应用    3
2.1.1数值例子    9
2.2    Shanks变换在级数收敛中的加速作用    12
2.2.1    Shanks变换在Floquet矢量模级数的混合加速算法中的应用    12
2.2.2    数值算例    14
2.2.3  Shanks变换在加速高速电路中周期结构电容参数计算中的作用    16
2.2.3    算例    16
3    结论    18
1    Shanks变换介绍
1.1    Shanks变换简介[1-3]

Shanks变换是一种加速收敛技术,应用于级数的处理,使得收敛更快.也应用于微分方程解的处理.
1.2    Shanks变换举例 Shanks变换及其应用+文献综述:http://www.lwfree.cn/shuxue/20190131/30188.html
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