Approximation of the pth Roots of a Matrix by Using Trapezoid Rule

Table 1

Comparison residual error for computing the 𝑝th root of Random matrix.

𝑝	Schur decomposition	Eigenvalue decomposition	Hessenberg decomposition
2	4.660633743656308𝑒−015	5.030320198311745𝑒−015	1.554377109452457𝑒−015
16	2.311964104013483𝑒−014	3.524734357427803𝑒−014	7.749850409855744𝑒−015
52	8.706212825269891𝑒−014	1.121352227197161𝑒−013	2.904341268646203𝑒−014
128	2.358332191022634𝑒−013	2.524139574310145𝑒−013	7.105511057327197𝑒−014
2012	3.448827113054843𝑒−012	3.472268532385117𝑒−012	1.170919968312386𝑒−012