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- W2070098148 abstract "Convergent methodology for ill-posed problems is typically equivalent to application of an operator dependent on a single parameter derived from the noise level and the data (a regularization parameter or terminal iteration number). In the context of a given problem discretized for purposes of numerical analysis, these methods can be viewed as resulting from imposed prior constraints bearing the same amount of information content. We identify a new convergent method for the treatment of certain multivariate ill-posed problems, which imposes constraints of a much lower information content (i.e., having much lower bias), based on the operator’s dependence on many data-derived parameters. The associated marked performance improvements that are possible are illustrated with solution estimates for a Lyapunov equation structured by an ill-conditioned matrix. The methodology can be understood in terms of a Minimax Entropy Principle, which emerges from the Maximum Entropy Principle in some multivariate settings." @default.
- W2070098148 created "2016-06-24" @default.
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- W2070098148 date "2009-01-08" @default.
- W2070098148 modified "2023-10-16" @default.
- W2070098148 title "Minimax entropy solutions of ill-posed problems" @default.
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- W2070098148 doi "https://doi.org/10.1090/s0033-569x-09-01120-7" @default.
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