Newton-Like Iteration Based on a Cubic Polynomial for Structured Matrices
Newton-Like Iteration Based on a Cubic Polynomial for Structured Matrices
复制标题
DOI：
10.1007/s11075-004-3996-z
复制
发表时间：
2004-08
影响因子：
2.1
通讯作者：
Gianni Codevico;V. Pan;M. Barel
中科院分区：
文献类型：
--
作者：
Gianni Codevico;V. Pan;M. Barel
我们回顾牛顿的迭代计算逆或Moore-Penrose广义逆矩阵。然后，我们专门这种方法的情况下，所有的输入，输出和中间辅助矩阵表示在一个压缩的形式，通过其短位移发电机的结构矩阵。我们设计了一种新的基于三次多项式的Newton迭代，并通过对Toeplitz类和Cauchy类矩阵的数值实验证明了它的有效性。
We recall Newton’s iteration for computing the inverse or Moore–Penrose generalized inverse of a matrix. Then we specialize this approach to the case of structured matrices where all input, output and intermediate auxiliary matrices are represented in a compressed form, via their short displacement generators. We design a new Newton-like iteration based on a cubic polynomial and show its effectiveness by some numerical experiments for matrices from the Toeplitz-like class and the Cauchy-like class.