## A study of Schr\"oder's method for the matrix \$p\$th root using power series expansions. (arXiv:1807.04251v1 [math.NA])

When \$A\$ is a matrix with all eigenvalues in the disk \$|z-1|&lt;1\$, the principal \$p\$th root of \$A\$ can be computed by Schr\"oder's method, among many other methods. In this paper we present a further study of Schr\"oder's method for the matrix \$p\$th root, through an examination of power series expansions of some sequences of scalar functions. Specifically, we obtain a new and informative error estimate for the matrix sequence generated by the Schr\"oder's method, a monotonic convergence result when \$A\$ is a nonsingular \$M\$-matrix, and a structure preserving result when \$A\$ is a nonsingular \$M\$-matrix or a real nonsingular \$H\$-matrix with positive diagonal entries.查看全文

## Solidot 文章翻译

 你的名字 留空匿名提交 你的Email或网站 用户可以联系你 标题 简单描述 内容 When \$A\$ is a matrix with all eigenvalues in the disk \$|z-1|<1\$, the principal \$p\$th root of \$A\$ can be computed by Schr\"oder's method, among many other methods. In this paper we present a further study of Schr\"oder's method for the matrix \$p\$th root, through an examination of power series expansions of some sequences of scalar functions. Specifically, we obtain a new and informative error estimate for the matrix sequence generated by the Schr\"oder's method, a monotonic convergence result when \$A\$ is a nonsingular \$M\$-matrix, and a structure preserving result when \$A\$ is a nonsingular \$M\$-matrix or a real nonsingular \$H\$-matrix with positive diagonal entries.