Abstract
This paper uses two simple variational data assimilation problems with the 1D viscous Burgers' equation on a periodic domain to investigate the impact of various diagonal-preconditioner update and scaling strategies, both on the limited-memory BFGS (Broyden, Fletcher, Goldfarb and Shanno) inverse Hessian approximation and on the minimization performance. These simple problems share some characteristics with the large-scale variational data assimilation problems commonly dealt with in meteorology and oceanography.
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