GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Fast secant methods for the iterative solution of large nonsymmetric linear systems
IMPACT of Computing in Science and Engineering
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Implicit coupling of partitioned fluid-structure interaction problems with reduced order models
Computers and Structures
The Quasi-Newton Least Squares Method: A New and Fast Secant Method Analyzed for Linear Systems
SIAM Journal on Numerical Analysis
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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.