{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,20]],"date-time":"2025-02-20T05:17:27Z","timestamp":1740028647755,"version":"3.37.3"},"reference-count":0,"publisher":"IOS Press","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018]]},"abstract":"<jats:p>Pipelined Krylov subspace methods achieve significantly improved parallel scalability compared to standard Krylov methods on present-day HPC hardware. However, this typically comes at the cost of a reduced maximal attainable accuracy. This paper presents and compares several stabilized versions of the communication-hiding pipelined Conjugate Gradients method. The main novel contribution of this work is the reformulation of the multi-term recurrence pipelined CG algorithm by introducing shifts in the recursions for specific auxiliary variables. These shifts reduce the amplification of local rounding errors on the residual. Given a proper choice for the shift parameter, the amplification of local rounding errors is reduced and the resulting algorithm improves the attainable accuracy. Numerical results on a variety of SPD benchmark problems compare different stabilization techniques for the pipelined CG algorithm, showing that the stabilized algorithms are able to attain a high accuracy while displaying excellent parallel performance.<\/jats:p>","DOI":"10.3233\/978-1-61499-843-3-77","type":"book-chapter","created":{"date-parts":[[2025,2,19]],"date-time":"2025-02-19T15:30:51Z","timestamp":1739979051000},"source":"Crossref","is-referenced-by-count":0,"title":["On Parallel Performance and Numerical Stability of Pipelined Conjugate Gradients"],"prefix":"10.3233","author":[{"family":"Cools Siegfried","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"family":"Vanroose Wim","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"7437","container-title":["Advances in Parallel Computing","Parallel Computing is Everywhere"],"original-title":[],"deposited":{"date-parts":[[2025,2,19]],"date-time":"2025-02-19T15:46:24Z","timestamp":1739979984000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.medra.org\/servlet\/aliasResolver?alias=iospressISBN&isbn=978-1-61499-842-6&spage=77&doi=10.3233\/978-1-61499-843-3-77"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018]]},"references-count":0,"URL":"https:\/\/doi.org\/10.3233\/978-1-61499-843-3-77","relation":{},"ISSN":["0927-5452"],"issn-type":[{"value":"0927-5452","type":"print"}],"subject":[],"published":{"date-parts":[[2018]]}}}