Approximate solutions for a finite moment problem (Q1123574)

The paper considers the problem of recovering a function \(u\in X_ n\), \(X_ n\) a finite dimensional subspace of \(L_ 2(0,1)\), from numbers \(\mu_ j\), \(\epsilon\), E satisfying \(\sum^{n}_{j=1}| \int^{1}_{0}x^{j-1}u(x)dx-\mu_ j|^ 2\leq \epsilon^ 2\), \(\sum^{n}_{j=1}\mu^ 2_ j>\epsilon^ 2\), \(\int^{1}_{0}(u'(x))^ 2dx\leq E^ 2\). In particular the case of step functions \(X_ n\) is dealt with. The paper gives upper and lower bounds for the condition number and discusses the stability in dependence of the distributions of the nodes of \(X_ n\).