Evaluation of the Capability of the Multigrid Method in Speeding Up the Convergence of Iterative Methods

<table>Smoothing the function <svg height="10.325" id="M47" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 11.225 10.325" width="11.225" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑇</tspan>
</text>
</g>
</g>
</svg> by GS iterations (<svg height="7.1374998" id="M48" style="vertical-align:-0.10033pt" version="1.1" viewbox="0 0 7.8874998 7.1374998" width="7.8874998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,7.1375)">
<g transform="translate(72,-66.29)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑛</tspan>
</text>
</g>
</g>
</svg>), convergence criterion = <svg height="14.375" id="M49" style="vertical-align:-0.3135pt" version="1.1" viewbox="0 0 54.099998 14.375" width="54.099998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.375)">
<g transform="translate(72,-60.5)">
<text transform="matrix(1,0,0,-1,-71.95,60.86)">
<tspan style="font-size: 12.50px; " x="0" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="9.0271664" y="0">×</tspan>
<tspan style="font-size: 12.50px; " x="19.804752" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="26.056252" y="0">0</tspan>
</text>
<text transform="matrix(1,0,0,-1,-39.64,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">−</tspan>
<tspan style="font-size: 8.75px; " x="5.99512" y="0">3</tspan>
</text>
</g>
</g>
</svg>.</table>

International Scholarly Research Notices

fig3

Figure 3

Figure 3: Evaluation of the Capability of the Multigrid Method in Speeding Up the Convergence of Iterative Methods 