Open AccessInference from Inadequate and Inaccurate Data, I
Author(s) -
George E. Backus
Publication year - 1970
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.011
H-Index - 771
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.65.1.1
Subject(s) - hilbert space , observer (physics) , inference , differentiable function , mathematics , section (typography) , norm (philosophy) , topological space , pure mathematics , discrete mathematics , computer science , physics , artificial intelligence , quantum mechanics , operating system , political science , law
Having measuredD numerical properties of a physical objectE which requires many more thanD parameters for its complete specification, an observer seeks to estimateP other numerical properties ofE . This paper describes how he can proceed whenE is adequately described by one membermE of a Hilbert space [unk] of possible models ofE , when he believes that the Hilbert norm ofmE is very likely rather smaller than some known numberM , and (except for section 6) when all the observed and sought-after properties ofE are continuous linear functionals on [unk]. Section 6 treats Frechet-differentiable non-linear functionals. A later paper will reduce unbounded functionals on arbitrary topological linear spaces to the present case.