Approximation of the <i>p</i>th Roots of a Matrix by Using Trapezoid Rule

<table>Residual error for computing <svg height="16.65" id="M183" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 30.875 16.65" width="30.875" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.012,0,0,-.012,12.525,8.425)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g><g transform="matrix(.012,0,0,-.012,18.236,8.425)"><path d="M368 703l-264 -866h-60l265 866h59z" id="x2F"></path></g><g transform="matrix(.012,0,0,-.012,23.139,8.425)"><path d="M570 304q0 -108 -87 -199q-40 -42 -94.5 -74t-105.5 -43q-41 0 -65 11l-29 -141q-9 -45 -1.5 -58t45.5 -16l26 -2l-5 -29l-241 -10l4 26q51 10 67.5 24t26.5 60l113 520q-54 -20 -89 -41l-7 26q38 28 105 53l11 49q20 25 77 58l8 -7l-17 -77q39 14 102 14q82 0 119 -36
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</svg> for Lehmer matrix.</table>

International Journal of Mathematics and Mathematical Sciences

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Figure 6

Figure 6: Approximation of the <i>p</i>th Roots of a Matrix by Using Trapezoid Rule 

International Journal of Mathematics and Mathematical Sciences

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

Figure 6