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Numerical analysis of iterative methods for solving evolution data assimilation problems. (English) Zbl 0963.65054
The authors investigate a data assimilation problem for an evolution problem. Here, the standard problem of numerically solving a differential equation is compounded by the need to approximate an unknown function in the initial data. After discretizing the problem, the authors consider different iterative methods for solving the differential equation. Utilizing examples these methods are then compared and contrasted.

65J10 Numerical solutions to equations with linear operators
35K15 Initial value problems for second-order parabolic equations
34G10 Linear differential equations in abstract spaces
65L05 Numerical methods for initial value problems involving ordinary differential equations
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