A Posteriori Analysis for Iterative Solvers for Nonautonomous Evolution Problems. Chaudhry, J., Estep, D., Ginting, V., & Tavener, S. SIAM/ASA Journal on Uncertainty Quantification, 3(1):434-459, 2015. ![A Posteriori Analysis for Iterative Solvers for Nonautonomous Evolution Problems [link]](https://bibbase.org/img/filetypes/link.svg "link")
Paper doi abstract bibtex We derive, implement, and test a posteriori error estimates for numerical methods for a nonautonomous linear system that involve iterative solution of the discrete equations. We consider two iterations: the Picard iteration and the Jacobi iteration for solving the discrete matrix-vector equations. To carry out the analysis, we define an appropriate adjoint problem for the numerical approximations using the matricant. We present a number of examples with interesting characteristics to illustrate the effectiveness of the estimate. We also present a comparison between the a posteriori error estimate and a conceptually simpler estimate obtained with a 'pseudoadjoint' problem.
@article {MR3354999,
AUTHOR = {Chaudhry, J. and Estep, D. and Ginting, V. and Tavener, S.},
TITLE = {A {P}osteriori {A}nalysis for {I}terative {S}olvers for {N}onautonomous
{E}volution {P}roblems},
JOURNAL = {SIAM/ASA Journal on Uncertainty Quantification},
VOLUME = {3},
YEAR = {2015},
NUMBER = {1},
PAGES = {434-459},
ISSN = {2166-2525},
MRCLASS = {65L05 (65L07 65L20 65L70)},
MRNUMBER = {3354999},
DOI = {10.1137/130949403},
URL = {http://dx.doi.org/10.1137/130949403},
ABSTRACT="We derive, implement, and test a posteriori error estimates for numerical methods for a nonautonomous linear system that involve iterative solution of the discrete equations. We consider two iterations: the Picard iteration and the Jacobi iteration for solving the discrete matrix-vector equations. To carry out the analysis, we define an appropriate adjoint problem for the numerical approximations using the matricant. We present a number of examples with interesting characteristics to illustrate the effectiveness of the estimate. We also present a comparison between the a posteriori error estimate and a conceptually simpler estimate obtained with a 'pseudoadjoint' problem."
}
Downloads: 0
{"_id":"4qLJcRgTHK8ttZzkk","bibbaseid":"chaudhry-estep-ginting-tavener-aposteriorianalysisforiterativesolversfornonautonomousevolutionproblems-2015","downloads":0,"creationDate":"2015-08-18T06:51:02.182Z","title":"A Posteriori Analysis for Iterative Solvers for Nonautonomous Evolution Problems","author_short":["Chaudhry, J.","Estep, D.","Ginting, V.","Tavener, S."],"year":2015,"bibtype":"article","biburl":"https://bibbase.org/network/files/3yQtKfRddpmAbuCJN","bibdata":{"bibtype":"article","type":"article","author":[{"propositions":[],"lastnames":["Chaudhry"],"firstnames":["J."],"suffixes":[]},{"propositions":[],"lastnames":["Estep"],"firstnames":["D."],"suffixes":[]},{"propositions":[],"lastnames":["Ginting"],"firstnames":["V."],"suffixes":[]},{"propositions":[],"lastnames":["Tavener"],"firstnames":["S."],"suffixes":[]}],"title":"A Posteriori Analysis for Iterative Solvers for Nonautonomous Evolution Problems","journal":"SIAM/ASA Journal on Uncertainty Quantification","volume":"3","year":"2015","number":"1","pages":"434-459","issn":"2166-2525","mrclass":"65L05 (65L07 65L20 65L70)","mrnumber":"3354999","doi":"10.1137/130949403","url":"http://dx.doi.org/10.1137/130949403","abstract":"We derive, implement, and test a posteriori error estimates for numerical methods for a nonautonomous linear system that involve iterative solution of the discrete equations. We consider two iterations: the Picard iteration and the Jacobi iteration for solving the discrete matrix-vector equations. To carry out the analysis, we define an appropriate adjoint problem for the numerical approximations using the matricant. We present a number of examples with interesting characteristics to illustrate the effectiveness of the estimate. We also present a comparison between the a posteriori error estimate and a conceptually simpler estimate obtained with a 'pseudoadjoint' problem.","bibtex":"@article {MR3354999,\n AUTHOR = {Chaudhry, J. and Estep, D. and Ginting, V. and Tavener, S.},\n TITLE = {A {P}osteriori {A}nalysis for {I}terative {S}olvers for {N}onautonomous\n {E}volution {P}roblems},\n JOURNAL = {SIAM/ASA Journal on Uncertainty Quantification},\n VOLUME = {3},\n YEAR = {2015},\n NUMBER = {1},\n PAGES = {434-459},\n ISSN = {2166-2525},\n MRCLASS = {65L05 (65L07 65L20 65L70)},\n MRNUMBER = {3354999},\n DOI = {10.1137/130949403},\n URL = {http://dx.doi.org/10.1137/130949403},\n ABSTRACT=\"We derive, implement, and test a posteriori error estimates for numerical methods for a nonautonomous linear system that involve iterative solution of the discrete equations. We consider two iterations: the Picard iteration and the Jacobi iteration for solving the discrete matrix-vector equations. To carry out the analysis, we define an appropriate adjoint problem for the numerical approximations using the matricant. We present a number of examples with interesting characteristics to illustrate the effectiveness of the estimate. We also present a comparison between the a posteriori error estimate and a conceptually simpler estimate obtained with a 'pseudoadjoint' problem.\"\n}\n\n","author_short":["Chaudhry, J.","Estep, D.","Ginting, V.","Tavener, S."],"key":"MR3354999","id":"MR3354999","bibbaseid":"chaudhry-estep-ginting-tavener-aposteriorianalysisforiterativesolversfornonautonomousevolutionproblems-2015","role":"author","urls":{"Paper":"http://dx.doi.org/10.1137/130949403"},"metadata":{"authorlinks":{"ginting, v":"https://bibbase.org/show?bib=https://bibbase.org/network/files/3yQtKfRddpmAbuCJN&msg=preview&fileId=3yQtKfRddpmAbuCJN"}},"downloads":0},"search_terms":["posteriori","analysis","iterative","solvers","nonautonomous","evolution","problems","chaudhry","estep","ginting","tavener"],"keywords":[],"authorIDs":["KGv5qNX2wproMHaMz"],"dataSources":["FMKDotGw9QMpa9Abz","x4GJj42ibi69jHYvw"]}