ON THE SIMILARITIES BETWEEN THE QUASI-NEWTON INVERSE LEAST SQUARES METHOD AND GMRES
We show how one of the best-known Krylov subspace methods, the generalized minimal residual method (GMRes), can be interpreted as a quasi-Newton method and how the quasi-Newton inverse least squares method (QN-ILS) relates to Krylov subspace methods in general and to GMRes in particular when applied...
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| Veröffentlicht in: | SIAM journal on numerical analysis 2010-01, Vol.47 (6), p.4660-4679 |
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| container_title | SIAM journal on numerical analysis |
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| creator | HAELTERMAN, ROB DEGROOTE, JORIS VAN HEULE, DIRK VIERENDEELS, JAN |
| description | We show how one of the best-known Krylov subspace methods, the generalized minimal residual method (GMRes), can be interpreted as a quasi-Newton method and how the quasi-Newton inverse least squares method (QN-ILS) relates to Krylov subspace methods in general and to GMRes in particular when applied to linear systems. We also show that we can modify QN-ILS in order to make it analytically equivalent to GMRes, without the need for extra matrix-vector products. |
| doi_str_mv | 10.1137/090750354 |
| format | Article |
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| subjects | Algebra Algebraic geometry Analogies Applied mathematics Approximation Equivalence Exact sciences and technology Inverse Iterative methods Jacobians Least squares method Linear algebra Linear and multilinear algebra, matrix theory Linear systems Mathematical analysis Mathematical models Mathematical theorems Mathematics Matrices Methods Numerical analysis Numerical analysis. Scientific computation Numerical linear algebra Perceptron convergence procedure Sciences and techniques of general use Secant function Subspace methods Theorems |
| title | ON THE SIMILARITIES BETWEEN THE QUASI-NEWTON INVERSE LEAST SQUARES METHOD AND GMRES |
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