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pro vyhledávání: '"CARSON, ERIN"'
The multigrid V-cycle method is a popular method for solving systems of linear equations. It computes an approximate solution by using smoothing on fine levels and solving a system of linear equations on the coarsest level. Solving on the coarsest le
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9b44960a66761fbf7dd803c1d333ca28
http://arxiv.org/abs/2306.06182
http://arxiv.org/abs/2306.06182
Autor:
Oktay, Eda, Carson, Erin
With the recent emergence of mixed precision hardware, there has been a renewed interest in its use for solving numerical linear algebra problems fast and accurately. The solution of total least squares problems, i.e., solving $\min_{E,f} \| [E, f]\|
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::32006da91187c87fc7792bba73391538
http://arxiv.org/abs/2305.19028
http://arxiv.org/abs/2305.19028
Autor:
Oktay, Eda, Carson, Erin
Publikováno v:
Programs and Algorithms of Numerical Mathematics 21.
With the emergence of mixed precision capabilities in hardware, iterative refinement schemes for solving linear systems $Ax=b$ have recently been revisited and reanalyzed in the context of three or more precisions. These new analyses show that under
Autor:
Carson, Erin, Daužickaitė, Ieva
We consider the split-preconditioned FGMRES method in a mixed precision framework, in which four potentially different precisions can be used for computations with the coefficient matrix, application of the left preconditioner, and application of the
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ab0c3df1a856b990db6fa4c6bae0adac
http://arxiv.org/abs/2303.11901
http://arxiv.org/abs/2303.11901
Autor:
Khan, Noaman, Carson, Erin
Hardware trends have motivated the development of mixed precision algo-rithms in numerical linear algebra, which aim to decrease runtime while maintaining acceptable accuracy. One recent development is the development of an adaptive precision sparse
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cc31ad13c3fbe2c77df96e82cc1731bf
The title of this paper is motivated by the title of the paper by Forsythe written in 1952 and published in Bull. Amer. Math. Soc., 59 (1953), pp. 299-329. Forsythe argues that solving a system of $n$ linear algebraic equations in $n$ unknowns is mat
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ed6b3b0e3326f7cfcdf679f1303d1cc6
http://arxiv.org/abs/2211.00953
http://arxiv.org/abs/2211.00953
Autor:
Oktay, Eda, Carson, Erin
Using lower precision in algorithms can be beneficial in terms of reducing both computation and communication costs. Motivated by this, we aim to further the state-of-the-art in developing and analyzing mixed precision variants of iterative methods.
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f194d7e08779b7bf329d44e0b6c9b891
http://arxiv.org/abs/2210.08839
http://arxiv.org/abs/2210.08839
Autor:
Carson, Erin, Khan, Noaman
With the commercial availability of mixed precision hardware, mixed precision GMRES-based iterative refinement schemes have emerged as popular approaches for solving sparse linear systems. Existing analyses of these approaches, however, are based on
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7386ff359a3e62100d61f8570f1028b2
http://arxiv.org/abs/2202.10204
http://arxiv.org/abs/2202.10204
The GMRES algorithm of Saad and Schultz (1986) is an iterative method for approximately solving linear systems $A{\bf x}={\bf b}$, with initial guess ${\bf x}_0$ and residual ${\bf r}_0 = {\bf b} - A{\bf x}_0$. The algorithm employs the Arnoldi proce
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::db566abfbbf230b65719f582d51e7b7e
Autor:
Carson, Erin, Daužickaitė, Ieva
Low rank matrix approximations appear in a number of scientific computing applications. We consider the Nyström method for approximating a positive semidefinite matrix $A$. In the case that $A$ is very large or its entries can only be accessed once,
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https://explore.openaire.eu/search/publication?articleId=doi_________::38cd01c863df08d9a06cc3a69ba17c6e