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Furthermore, we consider general nonsingular matrices, and we do not assume that all matrices are pairwise close or that the sequence of matrices converges to a particular matrix. Our methods work well under these general assumptions, and hence form a significant advancement with respect to related work in this area. We can reduce the cost of solving subsequent systems in the sequence by recycling selected subspaces generated for previous systems. We consider two approaches that allow for the continuous improvement of the recycled subspace at low cost. We consider both Hermitian and non\u2010Hermitian problems, and we analyze our algorithms both theoretically and numerically to illustrate the effects of subspace recycling. We also demonstrate the effectiveness of our algorithms for a range of applications from computational mechanics, materials science, and computational physics.<\/jats:p>","DOI":"10.1137\/040607277","type":"journal-article","created":{"date-parts":[[2006,10,23]],"date-time":"2006-10-23T11:30:55Z","timestamp":1161603055000},"page":"1651-1674","source":"Crossref","is-referenced-by-count":255,"title":["Recycling Krylov Subspaces for Sequences of Linear Systems"],"prefix":"10.1137","volume":"28","author":[{"given":"Michael L.","family":"Parks","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Eric","family":"de Sturler","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Greg","family":"Mackey","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Duane D.","family":"Johnson","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Spandan","family":"Maiti","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,10,6]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479801398608"},{"key":"R2","doi-asserted-by":"crossref","unstructured":"R. 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Medeke,\n                      Set QCD: Quantum Chromodynamics\n                      , description of matrix set on NIST Matrix Market, http:\/\/math.nist.gov\/MatrixMarket."},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479897321362"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827599364659"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(80)90247-5"},{"key":"R23","unstructured":"M. L. Parks,\n                      The Iterative Solution of a Sequence of Linear Systems Arising from Nonlinear Finite Element Analysis\n                      , Ph.D. thesis, Department of Computer Science, University of Illinois at Urbana\u2010Champaign, 2005."},{"key":"R24","doi-asserted-by":"crossref","unstructured":"M. L. 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