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Recycling Krylov Subspaces for Sequences of Linear Systems
 SIAM J. Sci. Comput
, 2004
"... Many problems in engineering and physics require the solution of a large sequence of linear systems. We can reduce the cost of solving subsequent systems in the sequence by recycling information from previous systems. We consider two dierent approaches. For several model problems, we demonstrate tha ..."
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Cited by 74 (6 self)
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Many problems in engineering and physics require the solution of a large sequence of linear systems. We can reduce the cost of solving subsequent systems in the sequence by recycling information from previous systems. We consider two dierent approaches. For several model problems, we demonstrate that we can reduce the iteration count required to solve a linear system by a factor of two. We consider both Hermitian and nonHermitian problems, and present numerical experiments to illustrate the eects of subspace recycling.
Recycling Subspace Information for Diffuse Optical Tomography
 SIAM J. Sci. Comput
, 2004
"... We discuss the efficient solution of a large sequence of slowly varying linear systems arising in computations for diffuse optical tomographic imaging. In particular, we analyze a number of strategies for recycling Krylov subspace information for the most efficient solution. We reconstruct threedim ..."
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Cited by 23 (4 self)
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We discuss the efficient solution of a large sequence of slowly varying linear systems arising in computations for diffuse optical tomographic imaging. In particular, we analyze a number of strategies for recycling Krylov subspace information for the most efficient solution. We reconstruct threedimensional...
THE ITERATIVE SOLUTION OF A SEQUENCE OF LINEAR SYSTEMS ARISING FROM NONLINEAR FINITE ELEMENT ANALYSIS
, 2005
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Gijzen, Iterative linear system solvers with approximate matrixvector products
 in QCD and Numerical Analysis III, Lect. Notes Comput. Sci
, 2005
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c ○ Copyright by Michael Lawrence Parks, 2005THE ITERATIVE SOLUTION OF A SEQUENCE OF LINEAR SYSTEMS ARISING FROM NONLINEAR FINITE ELEMENT ANALYSIS BY
"... iii Acknowledgments I am indebted to my advisor, Eric de Sturler, for guiding both my research and my professional development. Throughout my time at Illinois, he provided encouragement, sound advice, good teaching, good company, and lots of good ideas. I want to thank my committee members for their ..."
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iii Acknowledgments I am indebted to my advisor, Eric de Sturler, for guiding both my research and my professional development. Throughout my time at Illinois, he provided encouragement, sound advice, good teaching, good company, and lots of good ideas. I want to thank my committee members for their contributions to my graduate education. Additionally, I’m grateful to have been a participant in Mike Heath’s 491 seminar, which covered many topics not taught in any ordinary class. I also thank Bob Dodds and Philippe Geubelle for providing the motivation for much of this thesis, and for supplying numerous “realworld ” problems. I benefitted greatly from interactions with my fellow graduate students, especially Chris