Least squares polynomials in the complex plane and their use for solving nonsymmetric linear systems
Least squares polynomials in the complex plane and their use for solving nonsymmetric linear systems
复制标题
复平面中的最小二乘多项式及其在求解非对称线性系统中的用途
DOI：
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发表时间：
1987
期刊：
影响因子：
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通讯作者：
Y. Saad
中科院分区：
文献类型：
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作者：
Y. Saad
提出了一种计算复平面多边形区域上一类最小二乘多项式的算法。一个重要的应用，这种技术来解决大型稀疏线性系统被认为是。使用一般多边形区域代替椭圆的优点在于，椭圆区域可能不能准确地表示矩阵A的谱的凸船体。该算法的一个有吸引力的特点是，它不需要任何显式的数值积分。数值实验表明，基于最小二乘的方法求解线性方程组比基于Chebyshev的方法具有更好的竞争力，并且更可靠。
We propose an algorithm for computing a class of least squares polynomials on polygonal regions of the complex plane. An important application of this technique to solving large sparse linear systems is considered. The advantage of using general polygonal regions instead of ellipses as was done in previous work, is that elliptic regions may fail to accurately represent the convex hull of the spectrum of the matrix A. An attractive feature of the algorithm is that it does not explicitly require any numerical integration. Numerical experiments show that the least-squares based methods for solving linear systems are competitive with the Chebyshev based methods and are more reliable.