The Strong Convergence of Prediction-Correction and Relaxed Hybrid Steepest-Descent Method for Variational Inequalities

<table class="table-group" id="tab3"><tr><td><table class="table"><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td align="left" rowspan="2">Asymmetric matrix </td><td align="center" colspan="4"><svg height="15.1375" id="M225" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 52.974998 15.1375" width="52.974998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg></td></tr><tr class="thead"><td align="center" colspan="2">Condition <a href="https://static.hindawi.com/articles/aaa/volume-2013/515902/figures/#condition3.1">10</a></td><td align="center" colspan="2">Condition <a href="https://static.hindawi.com/articles/aaa/volume-2013/515902/figures/#condition3.2">12</a></td></tr><tr class="thead"><td align="left"><span style="width: 8.6625004px;"><svg height="7.9499998" id="M227" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 8.6625004 7.9499998" width="8.6625004" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path d="M495 86q-46 -47 -87 -72.5t-63 -25.5q-43 0 -16 107l49 210q7 34 8 50.5t-3 21t-13 4.5q-35 0 -109.5 -72.5t-115.5 -140.5q-21 -75 -38 -159q-50 -10 -76 -21l-6 8l84 340q8 35 -4 35q-17 0 -67 -46l-15 26q44 44 85.5 70.5t64.5 26.5q35 0 10 -103l-24 -98h2
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</svg></span></td><td align="center"> It </td><td align="center"> cpu</td><td align="center"> It </td><td align="center"> cpu </td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td align="left"> 1000</td><td align="center"> 193</td><td align="center"> 3893.63</td><td align="center"> 126</td><td align="center">2280.74 </td></tr><tr><td align="left">2000 </td><td align="center">318 </td><td align="center">42981.02</td><td align="center">200</td><td align="center">28737.65 </td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Numerical results for tolerance <svg height="16.049999" id="M224" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 29.762501 16.049999" width="29.762501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg>.

Abstract and Applied Analysis

tab3

Table 3

Table 3: The Strong Convergence of Prediction-Correction and Relaxed Hybrid Steepest-Descent Method for Variational Inequalities 