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In linear algebra, the order-r Krylov subspace generated by an n-by-n matrix A and a vector b of dimension n is the linear subspace spanned by the images of b under the first r powers of A (starting from A 0 = I {\displaystyle A^{0}=I} ), that is,
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| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Arnoldi iteration can be used for finding one | instance of | These tests are equivalent to finding the span of the Gramians associated with the system/output maps so the uncontrollable and unobservable subspaces are simply the orthogonal… | 0.80 | text |
| Krylov subspace | has method | The | 0.60 | section |
| Krylov subspace | has method | Krylov | 0.60 | section |
| Krylov subspace | has method | Conjugate | 0.60 | section |
| Krylov subspace | has method | IDR | 0.60 | section |
| Krylov subspace | has method | Induced | 0.60 | section |
| Krylov subspace | has method | GMRES | 0.60 | section |
| Krylov subspace | has method | BiCGSTAB | 0.60 | section |
| Krylov subspace | has method | QMR | 0.60 | section |
| Krylov subspace | has method | TFQMR | 0.60 | section |
| Krylov subspace | has method | MINRES | 0.60 | section |
| Krylov subspace | related to Further reading | Nevanlinna | 0.60 | section |
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