PUMA publications for /tag/sparse%20preconditionedhttps://puma.ub.uni-stuttgart.de/tag/sparse%20preconditionedPUMA RSS feed for /tag/sparse%20preconditioned2024-03-28T22:57:10+01:00Applying Efficient Fault Tolerance to Enable the Preconditioned Conjugate Gradient Solver on Approximate Computing Hardwarehttps://puma.ub.uni-stuttgart.de/bibtex/28b341984a107175be05eebdda39e6c12/clausbraunclausbraun2018-03-19T16:15:07+01:00AxC CCG PCG SimTech approximate computing conjugate error-correction error-detection fault-tolerance gradient linear myown preconditioned solver sparse systems <span data-person-type="author" class="authorEditorList "><span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Alexander Schöll" itemprop="url" href="/person/1819e882fc0ec03e0c6e332411bfbf42d/author/0"><span itemprop="name">A. Schöll</span></a></span>, </span><span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Claus Braun" itemprop="url" href="/person/1819e882fc0ec03e0c6e332411bfbf42d/author/1"><span itemprop="name">C. Braun</span></a></span>, </span> and <span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Hans-Joachim Wunderlich" itemprop="url" href="/person/1819e882fc0ec03e0c6e332411bfbf42d/author/2"><span itemprop="name">H. Wunderlich</span></a></span></span>. </span><span class="additional-entrytype-information"><span itemtype="http://schema.org/Book" itemscope="itemscope" itemprop="isPartOf"><em><span itemprop="name">Proceedings of the IEEE International Symposium on Defect and Fault Tolerance in VLSI and Nanotechnology Systems (DFT'16)</span>, </em></span><em>page <span itemprop="pagination">21-26</span>. </em>(<em><span>2016<meta content="2016" itemprop="datePublished"/></span></em>)</span>Mon Mar 19 16:15:07 CET 2018Proceedings of the IEEE International Symposium on Defect and Fault Tolerance in VLSI and Nanotechnology Systems (DFT'16)21-26{Applying Efficient Fault Tolerance to Enable the Preconditioned Conjugate Gradient Solver on Approximate Computing Hardware}2016AxC CCG PCG SimTech approximate computing conjugate error-correction error-detection fault-tolerance gradient linear myown preconditioned solver sparse systems A new technique is presented that allows to execute the preconditioned conjugate gradient (PCG) solver on approximate hardware while ensuring correct solver results. This technique expands the scope of approximate computing to scientific and engineering applications. The changing error resilience of PCG during the solving process is exploited by different levels of approximation which trade off numerical accuracy and hardware utilization. Such approximation levels are determined at runtime by periodically estimating the error resilience. An efficient fault tolerance technique allows reductions in hardware utilization by ensuring the continued exploitation of maximum allowed energy-accuracy trade-offs. Experimental results show that the hardware utilization is reduced on average by 14.5% and by up to 41.0% compared to executing PCG on accurate hardware.Low-Overhead Fault-Tolerance for the Preconditioned Conjugate Gradient Solverhttps://puma.ub.uni-stuttgart.de/bibtex/28c90a682adda1e125eb007f0c70bd70a/clausbraunclausbraun2018-03-19T16:15:07+01:00ABFT CG PCG SimTech conjugate error error-correction error-detection fault fault-tolerance gradient linear myown preconditioned solver sparse system <span data-person-type="author" class="authorEditorList "><span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Alexander Schöll" itemprop="url" href="/person/1d133c0d9eda7017c266a9d01721a9c91/author/0"><span itemprop="name">A. Schöll</span></a></span>, </span><span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Claus Braun" itemprop="url" href="/person/1d133c0d9eda7017c266a9d01721a9c91/author/1"><span itemprop="name">C. Braun</span></a></span>, </span><span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Michael A. Kochte" itemprop="url" href="/person/1d133c0d9eda7017c266a9d01721a9c91/author/2"><span itemprop="name">M. Kochte</span></a></span>, </span> and <span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Hans-Joachim Wunderlich" itemprop="url" href="/person/1d133c0d9eda7017c266a9d01721a9c91/author/3"><span itemprop="name">H. Wunderlich</span></a></span></span>. </span><span class="additional-entrytype-information"><span itemtype="http://schema.org/Book" itemscope="itemscope" itemprop="isPartOf"><em><span itemprop="name">Proceedings of the International Symposium on Defect and Fault Tolerance in VLSI and Nanotechnology Systems (DFT'15)</span>, </em></span><em>page <span itemprop="pagination">60-65</span>. </em>(<em><span>2015<meta content="2015" itemprop="datePublished"/></span></em>)</span>Mon Mar 19 16:15:07 CET 2018Proceedings of the International Symposium on Defect and Fault Tolerance in VLSI and Nanotechnology Systems (DFT'15)60-65{Low-Overhead Fault-Tolerance for the Preconditioned Conjugate Gradient Solver}2015ABFT CG PCG SimTech conjugate error error-correction error-detection fault fault-tolerance gradient linear myown preconditioned solver sparse system Linear system solvers are an integral part for many different compute-intensive applications and they benefit from the compute power of heterogeneous computer architectures. However, the growing spectrum of reliability threats for such nano-scaled CMOS devices makes the integration of fault tolerance mandatory. The preconditioned conjugate gradient (PCG) method is one widely used solver as it finds solutions typically faster compared to direct methods. Although this iterative approach is able to tolerate certain errors, latest research shows that the PCG solver is still vulnerable to transient effects. Even single errors, for instance, caused by marginal hardware, harsh environments, or particle radiation, can considerably affect execution times, or lead to silent data corruption. In this work, a novel fault-tolerant PCG solver with extremely low runtime overhead is proposed. Since the error detection method does not involve expensive operations, it scales very well with increasing problem sizes. In case of errors, the method selects between three different correction methods according to the identified error. Experimental results show a runtime overhead for error detection ranging only from 0.04% to 1.70%. Efficient On-Line Fault-Tolerance for the Preconditioned Conjugate Gradient Methodhttps://puma.ub.uni-stuttgart.de/bibtex/27e5f4629e5616459c867bc30d3893e78/clausbraunclausbraun2018-03-19T16:15:07+01:00ABFT CG PCG SimTech conjugate efficiency fault fault-tolerance gradient linear myown preconditioned solver sparse <span data-person-type="author" class="authorEditorList "><span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Alexander Schöll" itemprop="url" href="/person/17911878633d0e9fce50d136187cf87a4/author/0"><span itemprop="name">A. Schöll</span></a></span>, </span><span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Claus Braun" itemprop="url" href="/person/17911878633d0e9fce50d136187cf87a4/author/1"><span itemprop="name">C. Braun</span></a></span>, </span><span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Michael A. Kochte" itemprop="url" href="/person/17911878633d0e9fce50d136187cf87a4/author/2"><span itemprop="name">M. Kochte</span></a></span>, </span> and <span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Hans-Joachim Wunderlich" itemprop="url" href="/person/17911878633d0e9fce50d136187cf87a4/author/3"><span itemprop="name">H. Wunderlich</span></a></span></span>. </span><span class="additional-entrytype-information"><span itemtype="http://schema.org/Book" itemscope="itemscope" itemprop="isPartOf"><em><span itemprop="name">Proceedings of the 21st IEEE International On-Line Testing Symposium (IOLTS'15)</span>, </em></span><em>page <span itemprop="pagination">95--100</span>. </em>(<em><span>2015<meta content="2015" itemprop="datePublished"/></span></em>)</span>Mon Mar 19 16:15:07 CET 2018Proceedings of the 21st IEEE International On-Line Testing Symposium (IOLTS'15)95--100{Efficient On-Line Fault-Tolerance for the Preconditioned Conjugate Gradient Method}2015ABFT CG PCG SimTech conjugate efficiency fault fault-tolerance gradient linear myown preconditioned solver sparse Linear system solvers are key components of many scientific applications and they can benefit significantly from modern heterogeneous computer architectures. However, such nano-scaled CMOS devices face an increasing number of reliability threats, which make the integration of fault tolerance mandatory. The preconditioned conjugate gradient method (PCG) is a very popular solver since it typically finds solutions faster than direct methods, and it is less vulnerable to transient effects. However, as latest research shows, the vulnerability is still considerable. Even single errors caused, for instance, by marginal hardware, harsh operating conditions or particle radiation can increase execution times considerably or corrupt solutions without indication. In this work, a novel and highly efficient fault-tolerant PCG method is presented. The method applies only two inner products to reliably detect errors. In case of errors, the method automatically selects between roll-back and efficient on-line correction. This significantly reduces the error detection overhead and expensive re-computations.