Performance of partitioned procedures in fluid-structure interaction
Computers and Structures
On the Similarities Between the Quasi-Newton Inverse Least Squares Method and GMRes
SIAM Journal on Numerical Analysis
Letter to the editor: On the non-singularity of the quasi-Newton-least squares method
Journal of Computational and Applied Mathematics
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We present a new quasi-Newton method that can solve systems of equations of which no information is known explicitly and which requires no special structure of the system matrix, like positive definiteness or sparseness. The method builds an approximate Jacobian based on input-output combinations of a black box system, uses a rank-one update of this Jacobian after each iteration, and satisfies the secant equation. While it has originally been developed for nonlinear equations we analyze its properties and performance when applied to linear systems. Analytically, the method is shown to be convergent in $n+1$ iterations ($n$ being the number of unknowns), irrespective of the nature of the system matrix. The performance of this method is greatly superior to other quasi-Newton methods and comparable with GMRes when tested on a number of standardized test-cases.