论文标题
用于计算矩阵平方根的缩放固定点算法
Scaled Fixed Point Algorithm for Computing the Matrix Square Root
论文作者
论文摘要
本文解决了矩阵平方根问题的数值解决方案。通过重新安排非线性矩阵方程$ a -x^2 = 0 $并包含正尺度参数，提出了两个固定点迭代。这些建议只需要计算一个次要的一个矩阵逆，最多只能计算每个迭代的矩阵乘法。建立了全球收敛结果。关于几个测试问题的数值比较与文献中的一些现有方法证明了我们的提议的效率和有效性。
This paper addresses the numerical solution of the matrix square root problem. Two fixed point iterations are proposed by rearranging the nonlinear matrix equation $A - X^2 = 0$ and incorporating a positive scaling parameter. The proposals only need to compute one matrix inverse and at most two matrix multiplications per iteration. A global convergence result is established. The numerical comparisons versus some existing methods from the literature, on several test problems, demonstrate the efficiency and effectiveness of our proposals.
