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A numerical technique for geophysical data assimilation problems using Pontryagin’s principle and splitting-up method. (English) Zbl 0818.65057
Summary: Formulations of the observational data assimilation problem are given and methods for its solution that constructively use conjugate equations are described. On the basis of Pontryagin’s maximum principle, the initial problem of minimizing the quadratic functional, which is the difference between the solution and observational data, reduces to the spatial- temporal problem. The solution of a maximum-principle boundary value problem is constructed on the basis of the splitting-up method, which reduces a complex multidimensional problem to the sequence of problems with simpler operators.

MSC:
65K10 Numerical optimization and variational techniques
49M15 Newton-type methods
86A05 Hydrology, hydrography, oceanography
49J20 Existence theories for optimal control problems involving partial differential equations
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