A Novel Parallel Algorithm Based on the Gram-Schmidt Method for Tridiagonal Linear Systems of Equations

<table>The speedup comparison between proposed algorithm and Cycle Reduction in two different orders of system of equations: (a) <svg height="6.4124999" id="M136" style="vertical-align:-0.09pt" version="1.1" viewbox="0 0 7.0875001 6.4124999" width="7.0875001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,6.4125)">
<g transform="translate(72,-66.87)">
<text transform="matrix(1,0,0,-1,-71.95,67.01)">
<tspan style="font-size: 11.21px; " x="0" y="0">𝑛</tspan>
</text>
</g>
</g>
</svg> = 200 000 and (b) <svg height="6.4124999" id="M137" style="vertical-align:-0.09pt" version="1.1" viewbox="0 0 7.0875001 6.4124999" width="7.0875001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,6.4125)">
<g transform="translate(72,-66.87)">
<text transform="matrix(1,0,0,-1,-71.95,67.01)">
<tspan style="font-size: 11.21px; " x="0" y="0">𝑛</tspan>
</text>
</g>
</g>
</svg> = 400 000.</table>

Mathematical Problems in Engineering

fig12

Figure 12

Figure 12: A Novel Parallel Algorithm Based on the Gram-Schmidt Method for Tridiagonal Linear Systems of Equations 