A Fine-grained Task Based Parallel Programming Paradigm of Gauss-Jordan Algorithm

Abstract

<!-- st1:*{behavior:url(#ieooui) } --><span style="font-size: 10pt; font-family: ";Times New Roman";;" lang="EN-US">Large scale matrix inversion has been widely used in many scientific</span><span style="font-size: 10pt; font-family: ";Times New Roman";;" lang="EN-US"> </span><span style="font-size: 10pt; font-family: ";Times New Roman";;" lang="EN-US">research domains</span><span style="font-size: 10pt; font-family: ";Times New Roman";;" lang="EN-US">.</span><span style="font-size: 10pt; font-family: ";Times New Roman";;" lang="EN-US"> </span><span style="font-size: 10pt; font-family: ";Times New Roman";;" lang="EN-US">A</span><span style="font-size: 10pt; font-family: ";Times New Roman";;" lang="EN-US">s a classical method of large matrix</span><span style="font-size: 10pt; font-family: ";Times New Roman";;" lang="EN-US"> </span><span style="font-size: 10pt; font-family: ";Times New Roman";;" lang="EN-US">inversion, block-based Gauss-Jordan (BbGJ) algorithm has</span><span style="font-size: 10pt; font-family: ";Times New Roman";;" lang="EN-US"> aroused</span><span style="font-size: 10pt; font-family: ";Times New Roman";;" lang="EN-US"> great </span><span style="font-size: 10pt; font-family: ";Times New Roman";;" lang="EN-US">concern</span><span style="font-size: 10pt; font-family: ";Times New Roman";;" lang="EN-US"> </span><span style="font-size: 10pt; font-family: ";Times New Roman";;" lang="EN-US">among</span><span style="font-size: 10pt; font-family: ";Times New Roman";;" lang="EN-US"> many researchers. </span><span style="font-size: 10pt; font-family: ";Times New Roman";;" lang="EN-US">Many </span><span style="font-size: 10pt; font-family: ";Times New Roman";;" lang="EN-US">people </span><span style="font-size: 10pt; font-family: ";Times New Roman";;" lang="EN-US">have developed parallel versions</span><span style="font-size: 10pt; font-family: ";Times New Roman";;" lang="EN-US"> of BbGJ. But large granularity based</span><span style="font-size: 10pt; font-family: ";Times New Roman";;" lang="EN-US"> </span><span style="font-size: 10pt; font-family: ";Times New Roman";;" lang="EN-US">task parallel</span><span style="font-size: 10pt; font-family: ";Times New Roman";;" lang="EN-US">ism </span><span style="font-size: 10pt; font-family: ";Times New Roman";;" lang="EN-US">(intra-iterative data dependence based tasks parallelism)</span><span style="font-size: 10pt; font-family: ";Times New Roman";;" lang="EN-US"> </span><span style="font-size: 10pt; font-family: ";Times New Roman";;" lang="EN-US">disables mapping more tasks on computing resources</span><span style="font-size: 10pt; font-family: ";Times New Roman";;" lang="EN-US"> </span><span style="font-size: 10pt; font-family: ";Times New Roman";;...