Geometrical Inverse Preconditioning for Symmetric Positive Definite Matrices
We focus on inverse preconditioners based on minimizing F ( X ) = 1 − cos ( X A , I ) , where X A is the preconditioned matrix and A is symmetric and positive definite. We present and analyze gradient-type methods to minimize F ( X ) on a suitable compact set. For this, we use...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2016-07-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | http://www.mdpi.com/2227-7390/4/3/46 |
| Summary: | We focus on inverse preconditioners based on minimizing F ( X ) = 1 − cos ( X A , I ) , where X A is the preconditioned matrix and A is symmetric and positive definite. We present and analyze gradient-type methods to minimize F ( X ) on a suitable compact set. For this, we use the geometrical properties of the non-polyhedral cone of symmetric and positive definite matrices, and also the special properties of F ( X ) on the feasible set. Preliminary and encouraging numerical results are also presented in which dense and sparse approximations are included. |
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| ISSN: | 2227-7390 |