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- W4224778813 abstract "For G∈Rm×n and g∈Rm, the minimization min∥Gψ−g∥2, with ψ∈Rn, is known as the Tykhonov regularization. We transport the Tykhonov regularization to an infinite-dimensional setting, that is min∥T(h)−k∥, where T:H→K is a continuous linear operator between Hilbert spaces H,K and h∈H,k∈K. In order to avoid an unbounded set of solutions for the Tykhonov regularization, we transform the infinite-dimensional Tykhonov regularization into a multiobjective optimization problem: min∥T(h)−k∥andmin∥h∥. We call it bounded Tykhonov regularization. A Pareto-optimal solution of the bounded Tykhonov regularization is found. Finally, the bounded Tykhonov regularization is modified to introduce the precise Tykhonov regularization: min∥T(h)−k∥with∥h∥=α. The precise Tykhonov regularization is also optimally solved. All of these mathematical solutions are optimal for the design of Magnetic Resonance Imaging (MRI) coils." @default.
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- W4224778813 date "2022-04-26" @default.
- W4224778813 modified "2023-09-25" @default.
- W4224778813 title "Analytical Solutions to Minimum-Norm Problems" @default.
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- W4224778813 doi "https://doi.org/10.3390/math10091454" @default.
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