Toeplitz Preconditioners for Toeplitz Systems with Nonnegative Generating Functions
Toeplitz Preconditioners for Toeplitz Systems with Nonnegative Generating Functions
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DOI：
10.1093/imanum/11.3.333
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发表时间：
1991-07
影响因子：
2.1
通讯作者：
R. Chan
中科院分区：
文献类型：
--
作者：
R. Chan
利用预条件共轭梯度法求解Toeplitz系统Tn x = B，其中n阶Toeplitz矩阵Tn的母函数是定义在[−π，π]中的连续非负周期函数.预条件Cn是带宽与n无关的带Toeplitz矩阵。我们证明了Cn-1 Tn的谱由与n无关的常数一致有界.特别地，我们证明了Tnx = b的解可以在O（nlogn）的运算中得到。
The preconditioned conjugate gradient method is employed to solve Toeplitz systems Tnx= b where the generating functions of then-by-nToeplitz matricesTnare continuous nonnegative periodic functions defined in [−π,π]. The preconditionedCnare band Toeplitz matrices with band-widths independent ofn. We prove that the spectra ofCn-1Tnare uniformly bounded by constants independent ofn. In particular, we show that the solutions ofTnx=bcan be obtained inO(nlogn) operations.