Low-rank approximate inverse for preconditioning tensor-structured linear systems (Q6486759)
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scientific article; zbMATH DE number 6370170
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Low-rank approximate inverse for preconditioning tensor-structured linear systems |
scientific article; zbMATH DE number 6370170 |
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Low-rank approximate inverse for preconditioning tensor-structured linear systems (English)
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17 November 2014
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The paper deals with the construction of low-rank preconditioners for equations in tensor format, yielding preconditioned equations NEWLINE\[NEWLINE PAu = Pb, NEWLINE\]NEWLINE with a preserved low-rank tensor format. For this purpose the authors use an updated greedy algorithm for the minimization of a suitable distance to \(A^{-1}\), by using Tucker or hierarchical Tucker format. Numerical experiments are provided for a high dimension Poisson equation and a stochastic partial differential equation.
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high dimension
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linear system
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preconditioning
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approximate inverse
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low rank
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hierarchical Tucker tensor
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tensor format
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greedy algorithm
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numerical experiment
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Poisson equation
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stochastic partial differential equation
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