Ciulli, S.; Mounsif, M.; Gorman, N.; Spearman, T. D. On the application of maximum entropy to the moments problem. (English) Zbl 0763.41004 J. Math. Phys. 32, No. 7, 1717-1719 (1991). Reconstruction of a function \(f(x)\) from a finite set of its moments \(\int_ 0^ 1 x^ n f(x)dx\) when the condition of maximum entropy is imposed as a constraint was dealt with starting from imprecise data with errors specified by a \(\chi^ 2\)-function. The entropy for \(f(x)\) is defined as \[ S[p]=-\int_ 0^ 1 p(x)\ln p(x)dx,\quad\text{where}\quad p(x)=f(x)\left(\int_ 0^ 1 f(x)dx\right)^{-1}. \] The first \(N\) moments are \(\mu_ n=\int_ 0^ 1 x^ n p(x)dx\), \(n=1\) to \(N\), they are associated with errors \(\varepsilon_ n\). The solution \(p(x)\) is of the polynomial form \(p(x)=\exp(a_ 0+a_ 1 x+\dots+a_ n x^ n)\), the coefficients \(a_ 0,a_ 1,\dots,a_ n\) are found by a set of algebraic equations. An extension of the method is discussed by the first author, F. Genet and G. Mennesier [Phys. Rev. D 36, 3494-3501 (1987)]. Reviewer: V.Burjan (Praha) Cited in 4 Documents MSC: 41A10 Approximation by polynomials 81V99 Applications of quantum theory to specific physical systems Keywords:approximation with constraints; moments; entropy PDFBibTeX XMLCite \textit{S. Ciulli} et al., J. Math. Phys. 32, No. 7, 1717--1719 (1991; Zbl 0763.41004) Full Text: DOI References: [1] DOI: 10.1016/0021-9991(79)90102-5 · Zbl 0406.65034 · doi:10.1016/0021-9991(79)90102-5 [2] DOI: 10.1063/1.526446 · doi:10.1063/1.526446 [3] DOI: 10.1063/1.528812 · Zbl 0782.65010 · doi:10.1063/1.528812 [4] DOI: 10.1103/PhysRevD.36.3494 · doi:10.1103/PhysRevD.36.3494 [5] DOI: 10.1007/BF02902727 · doi:10.1007/BF02902727 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.